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4-1992

Spatial Visualization and Leadership in Teaching Multiview Orthographic Projection: An Alternative to the Glass Box

Mark A. Curtis Western Michigan University

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Recommended Citation Curtis, Mark A., "Spatial Visualization and Leadership in Teaching Multiview Orthographic Projection: An Alternative to the Glass Box" (1992). Dissertations. 1936. https://scholarworks.wmich.edu/dissertations/1936

This Dissertation-Open Access is brought to you for free and open access by the Graduate College at ScholarWorks at WMU. It has been accepted for inclusion in Dissertations by an authorized administrator of ScholarWorks at WMU. For more information, please contact [email protected]. SPATIAL VISUALIZATION AND LEADERSHIP IN TEACHING MULTIVIEW ORTHOGRAPHIC PROJECTION: AN ALTERNATIVE TO THE GLASS BOX

by

Mark A. Curtis

A Dissertation Submitted to the Faculty of The Graduate College in partial fulfillment of the requirements for the Degree of Doctor of Education Department of Educational Leadership

Western Michigan University Kalamazoo, Michigan April 1992

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SPATIAL VISUALIZATION AND LEADERSHIP IN TEACHING MULTIVIEW ORTHOGRAPHIC PROJECTION: AN ALTERNATIVE TO THE GLASS BOX

Mark A. Curtis, Ed.D.

Western Michigan University, 1992

The purpose of this study was to compare the effectiveness of

using one instructional method versus another in teaching multiview

orthographic projection to college students possessing varied spa­

tial visualization abilities. Two instructional methods were used:

(1) the traditional hinged glass box method and (2) an unconven­

tional method in which an object is placed in the middle of a bowl/

hemispheric shape where the front view of the object is seen by

looking directly into the bowl. Other views are developed by slid­

ing the object along the surface of the bowl until they are at right

angle to the viewer's line of sight. The independent variable

manipulated was the instructional method and the dependent variable

was the spatial visualization development of students as demon­

strated through their a b ility to mentally solve complex multiview

orthographic projection problems.

The subjects were mostly freshmen and sophomores majoring in

engineering technology enrolled in two intact basic engineering

graphics classes at Ferris State University, Big Rapids, Michigan.

The sample size was 92. The Differential Aptitude Test, Space Rela­

tions: Form T (DAT-SR-T, Bennett, Seashore, & Wesman, 1972) was

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. administered to all subjects. Scores attained on the DAT-SR-T were

used to divide the subjects into three groups and four visualization

aptitude levels. Subjects were also given a 12-item pretest for

multiview orthographic projection knowledge, taken from the Western

Michigan University (Kalamazoo) Career Guidance Inventory Part 4

(Nowak, Walter, Vander Ark, & Henry, 1980).

Group 1 received 2 hours of instruction using glass box

imagery, Group 2 received 2 hours of bowl imagery, and Group 3 re­

ceived no formal orthographic instruction. Hypotheses were formu­

lated and tested for significant differences between treatment and

control groups for each aptitude level. The 12-item orthographic

test was given to all subjects to record spatial visualization abil­

ity gains. The data collected were analyzed using the Statistical

Package of Social Sciences (SPSS, Inc., 1990) software, Release 4.1.

No significant difference in spatial visualization gain scores was

found between treatment groups or aptitude levels at the .05 level.

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Spatial visualization and leadership in teaching multiview orthographic projection: An alternative to the glass box

Curtis, Mark A., Ed.D.

Western Michigan University, 1992

UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS

During the preparation of this dissertation, I have been given

guidance and support by many individuals and organizations. I wish

to give special thanks to my advisor and committee chairman, Dr.

Kenneth Dickie for his assistance, direction, and support over the

past 6 years; and to my committee members, Dr. David Cowden and Dr.

Richard Munsterman, for their recommendations and advice. Also,

appreciation is expressed to Dr. Edgar Kelley and Dr. Uldis

Smidchens for their encouragement during the developmental stages of

my dissertation proposal writing.

Mark Nickel of Western Michigan University's Human Subjects

Institutional Review Board was also very helpful. Dr. Gerard Nowak

also gave many fine suggestions and much assistance relating to

instrumentation and methodology. Dr. Fred Swartz of Ferris State

University is also much appreciated for his help in evaluation of

the research findings. I am also thankful that Lee Pakko w illingly

agreed to take on the task of typing. The Administration of Ferris

State University is appreciated for the support they provided me

through a one-term sabbatical leave.

I also wish to thank many of my close friends for their moral

support, especially Virginia VanWie, Dr. Janet Towne, Doug and Ellen

Haneline, Manuel and Eloisa Puerta, and David Murray. And fin a lly,

I am most grateful for the love and encouragement given to me by my

i i

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgments--Continued

parents, Lawrence and Marlene Curtis; my children, Aaron and Leah

and my wife, Margaret, during the completion of this study.

Mark A. Curtis

i ii

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS

ACKNOWLEDGMENTS ...... ii

LIST OF TABLES ...... vii

LIST OF FIGURES ...... ix

CHAPTER

I. INTRODUCTION ...... 1

Purpose of the Study ...... 3

The Variables ...... 3

Educational Leadership ...... 4

Need for the Study ...... 5

The Scope and Limits of the Study ...... 8

II. RELEVANT LITERATURE ...... 9

Comparative Instructional Methods ...... 9

Summary of Research on Instructional Methods ...... 17

Studies of Individual Cognitive Difference ...... 18

Summary of Research on Cognitive Characteristies ... 21

Psychological Constructs ...... 21

Summary of Research on PsychologicalConstructs . . . . 23

The Hinged Glass Box ...... 23

The Bowl/Hemisphere ...... 24

Hypotheses ...... 27

Primary Research Hypotheses ...... 28

Secondary Research Hypotheses ...... 29

A Final Comment ...... 29

iv

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents--Continued

CHAPTER

I I I . RESEARCH DESIGN AND METHODOLOGY ...... 30

Population ...... 30

Research Design ...... 30

Pretest for Spatial Visualization Ability ...... 31

Pretest for Orthographic Projection Knowledge ... 36

Design of Treatment ...... 36

The Posttest ...... 39

Insuring Subject Confidentiality ...... 39

Threats to V a lid it y ...... 40

An Ethical Concern ...... 41

Data Analysis ...... 41

IV. FINDINGS ...... 43

Primary Research Hypotheses ...... 52

Secondary Research Hypotheses ...... 55

Summary...... 59

V. CONCLUSIONS AND RECOMMENDATIONS ...... 61

Pretesting for Spatial Visualization Ability ...... 62

Pretesting for Multiview Orthographic Projection Ab i 1 i ty ...... 63

Primary Research Hypotheses ...... 64

Secondary Research Hypotheses ...... 66

Spatial Visualization Imagery ...... 68

Recommendations for Further Study ...... 69

v

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents--Continued

APPENDICES ...... 71

A. Definition of Terms ...... 72

B. Recruitment Script ...... 76

C. Consent Form ...... 78

D. Differential Aptitude Test Space Relations Form T Directions and Examples ...... 80

E. Western Michigan University Diagnostic/Achievement Quiz, Spatial Perception, Directions, and Example ...... 84

F. Correlation Data for Two Pretests ...... 88

G. Pretest/Posttest/Gain for Standard Deviation Calculation Data ...... 92

H. Complete Raw Data by Subject, Test, Group, and Aptitude Level ...... 96

I. Approval Letter From Western Michigan University Human Subjects Institutional Review Board ...... 100

BIBLIOGRAPHY ...... 102

vi

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF TABLES

1. Frequency Distribution of the DAT-SR-T Scores ...... 32

2. DAT-SR-T Raw Score Test Results by Group ...... 34

3. Comparison Table of DAT-SR-T Pretest Scores and Orthographic Spatial Perception Pretest Scores by Individual Subject and Group ...... 37

4. Group 1 (Hinged Glass Box Imagery) Treatment Effect Data by Aptitude Level ...... 43

5. Group 2 (Bowl/Hemisphere Imagery) Treatment Effect Data by Aptitude Level ...... 46

6. Group 3 (No Instructional Treatment) Treatment Effect Data ...... 48

7. Summary of DAT-SR-T Pretest by Group ...... 50

8. Analysis of Variance for Equality of Spatial Visualization Aptitude Between Groups 1, 2, and 3 ...... 50

9. Summary of Orthographic Pretest Scores by Group ...... 51

10. Comparisons of Posttreatment Gains of Low Aptitude Visualizers Between Instructional Treatments ...... 52

11. Comparisons of Posttreatment Gains of Middle Low Aptitude Visualizers Between Instructional Treatments ...... 53

12. Comparisons of Posttreatment Gains of Middle High Aptitude Visualizers Between Instructional Treatment ...... 54

13. Comparisons of Posttreatment Gains of High Aptitude Visualizers Between Instructional Treatments ...... 55

14. Posttreatment Visualization Gains Summary ...... 56

15. Analysis of Variance for Gain Score Comparisons Between Groups 1, 2, and 3 ...... 56

vi i

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Tables—Continued

16. Mean Scores by Aptitude Level for the Glass Box Treatment Group ...... 57

17. Analysis of Variance for Gain Score Comparisons Between Aptitude Levels Within Group 1 ...... 57

18. Mean Scores by Aptitude Level for the Bowl/Hemisphere Treatment Group ...... 58

19. Analysis of Variance for Gain Score Comparisons Between Aptitude Levels Within Group 2 ...... 59

v i i i

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES

1. The Hinged Glass Box ...... 25

2. The Bowl/Hemisphere ...... 26

ix

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER I

INTRODUCTION

Ancient cave paintings found around the world provide evidence

that our earliest human ancestors communicated to themselves, to one

another, to their deities, and to future generations through mural

art (Samuels, 1975). Many three-dimensional objects and animals

found in their lives were drawn in picture form on rock walls, a

two-dimensional medium. These early drawings seem to lack depth

because items were drawn as if viewed head-on. And although objects

are rarely viewed from precisely 90 degrees, they are always per­

ceived that way. In perceptual reality a circle is seen as a

circle, not an ellipse (McKim, 1980a, 1980b). The modern graphic

equivalent of seeing things in this head-on way is orthographic

projection, a formal method of drawing typically used by drafters

and designers.

The firs t recorded use of multiview orthographic projection was

by Albrecht Durer, a German painter and engraver, in his 1525 work

that defined the proportions of the human body and its individual

parts (Booker, 1963). In his book, Durer drew the human head in

third angle projection and the feet in first angle projection.

These two orthographic projection styles are s till both used today

with North America using third angle and Europe using firs t angle

projection.

1

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Later in 1795 Gaspard Monge systematized all drawing into a

science called La Geometrie Descriptive. The glass box, planes of

projection, fold lines, direct views, and other methods designed to

aid in spatial visualization are simply methods of presenting the

graphic science developed by Monge (Bertoline, 1991).

Due to the confusion caused by differences in firs t and third

angle projection, in 1883 Joshua Rose wrote a book that established

indirect and direct revolution as applied to orthographic projection

or to the arrangement of views in multiview drawing (Booker, 1963).

Yet, to this day the conceptualizing of three-dimensional geometry

and transforming it to a two-dimensional medium is found to be a

d iffic u lt process for many students of engineering and technology

(Ross, 1991).

Piaget discovered that the ability to distinguish between and

coordinate possible geometric perspectives accurately does not ap­

pear in children until age 9 or 10 (Pulaski, 1980). For those that

choose to enter many engineering and technical professions, the

ab ility to spatially visualize geometry must be further developed.

In a study by El wood (1979), 22 mechanical engineering practitioners

were asked to hierarchically rank 70 skills commonly used in their

profession. They, as a group, ranked the abilities of shape visual­

ization and multiview representation as most important. This rank­

ing was also confirmed for manufacturing engineers in a study by

Curtis (1983).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3

Purpose of the Study

The purpose of this study was to compare the effectiveness of

using one instructional method versus another when teaching multi­

view orthographic projection to college students majoring in engi­

neering technology. The principal aim was to judge the relative

worth of two instructional methodologies, one traditional, the

hinged glass box (see definition, Appendix A) presently in use, and

one nontraditional, the bowl/hemispheric method of spatial visuali­

zation (see definition, Appendix A). A further aim of the study was

to determine if students with and without demonstrated spatial visu­

alization abilities ( i.e ., visual and nonvisual) show greater visual

development when exposed to one instructional method versus another.

The Variables

Therefore, the independent variable manipulated in this study

was the instructional method used in the teaching of orthographic

projection. The dependent variable was, in turn, the spatial visu­

alization development of students as demonstrated through their

a b ility to mentally solve complex multiview orthographic projection

problems.

The study focused on whether or not the nontraditional method

of spatial visualization should be used in place of the traditional

method in order to optimize student learning. Information was gath­

ered about the characteristies of students in each instructional

treatment, the amount of gain ( i.e ., development) in multiview

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. orthographic knowledge under each treatment, and the advisability of

spatial visualization ab ility sectioning (i.e ., pretesting) for

different methodologies.

Educational Leadership

From the very conception of this research study, a contribution

to leadership in engineering graphics education was the desired

outcome. Leadership, of course, is not mere power holding; leader­

ship serves ultimately in some way to release human potential

(Burns, 1978). Any instructional method that is proved to be supe­

rior to another will unlock human potential if used. Leaders in all

situations are interested in fresh choices and move to act as agents

of change (Bennis & Nanus, 1985). A new instructional method offers

leaders in engineering graphics education this type of neoteric

choice. Meaningful and effective spatial research related to engi­

neering graphics is lacking (C. L. M iller & Bertoline, 1989). The

published results of this study may encourage change and further

experimentation.

A partial lis t of individuals involved in engineering graphics

education who will be interested in the results of this study is

shown below.

1. Researchers specializing in the study of engineering graph­

ics, spatial visualization, and related fields.

2. Deans of engineering and technology schools.

3. Chairs of departments in which engineering graphics is

taught.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4. Corporate training directors considering personnel training

in the area of blueprint reading.

This study will be of special interest to engineering deans and

department chairs who often find themselves cast in the role of

curriculum or instructional manager. In this supervisory role they

must help the faculty find ways to more effectively deliver existing

technical material. The increased instructional effectiveness is

required to make room within the curriculum for an ever expanding

technological knowledge base.

Each of the aforementioned categories of individuals is inter­

ested in the effectiveness of the instructional methods used within

the groups, areas, and programs they lead. Effectiveness, in this

context, is defined as accomplishing a goal (Bogue, 1985). And here

the goal is effective instruction in multiview orthographic projec­

tion. Effectiveness is how leaders measure success (Bennis & Nanus,

1985).

Finally, leaders do not think short term (Naisbitt, 1984).

Educational research of all types is completed today for some future

benefit to society in general, again making those engaged in this

activity leaders.

Need for the Study

During the era from 1920 to 1960 the typical bachelor's degree

in engineering or technology contained 15 semester hours of

coursework devoted to freehand sketching, mechanical drawing, and

spatial visualization (Raudebaugh, 1988). Russia's Sputnik I,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. launched October 4, 1957, sent shock waves throughout the American

educational system. Science and engineering education were seen as

a not so hidden space weapon. In 1959 Russia graduated 86,000

scientists to 36,000 engineers in the United States (Cox, 1962).

Immediately, college engineering and technology curriculums began to

increase the amount of mathematics and science required while de­

emphasizing traditional subjects such as drawing and machine shop

(P. W. M iller, 1988).

Today the Accreditation Board for Engineering and Technology

(ABET) stipulates that a B.S. degree in engineering or technology

must contain a minimum of 124 semester hours (ABET, 1989). ABET

also specifies the curricular content of accredited programs. As

Raudebaugh (1988) found, engineering design graphics is taught in

and limited to one 3 credit hour course. Over the past 30 years,

colleges of engineering and technology have been required to teach

spatial visualization through multiview orthographic projection in

80% less time to larger numbers of students with poor visualization

skills. Bertoline (1990), in a comment in the Engineering Design

Graphics Journal, wrote:

Visualization instruction in engineering design graphics is important because visualization is not formally taught at any level of education in the United States. High visualization ab ility is the most important prerequisite cognitive process that a student must have to be success­ ful in representing three-dimensional objects on two- dimensional media, (pp. 63-64)

Given the importance of spatial visualization knowledge coupled

with limited instructional time, new levels of instructional effec­

tiveness must be found, and nontraditional methods must be tried.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Furthermore, Wiley (1990) indicated engineering design graphics

courses are coming under increased scrutiny; the need to improve

visualization becomes the chief concern as it is a fundamental skill

that directly affects many areas of engineering education and manu­

facturing productivity.

In a study conducted by Lajoie (1986), no evidence was found

that spatial visualization can be taught to all individuals and

transferred to a test. Cronbach and Snow (1981) stated the belief

that techniques for teaching spatial visualization, such as the

hinged glass box, are simply "mental prostheses" (p. 282) for the

student with poor visualization ability. In other words, the glass

box does the spatial reasoning for the individual. Yet, the glass

box visualization technique does not work for all students. Certain

underlying psychological characteristics used in spatial visualiza­

tion indicate that the bowl/hemispheric instructional method holds

promise for use in teaching orthographic projection. These psycho­

logical characteristics which include, among others, cone of vision

and tracking are more fu lly covered in Chapter II.

Over the next 10 years, engineering design graphics will be

taught to 500,000 future graduates of engineering schools (Barr &

Juricic, 1991). Another visualization technique used either in

addition to, or in place of, the glass box may enhance the visuali­

zation ab ility, and in turn the productivity, of these graduates.

Also, many students with nonvisual cognitive learning styles may

have been helped to succeed had they been exposed to the bowl/hemi­

spheric spatial visualization technique.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. One symptom of a curriculum problem is when students are per­

forming poorly on standardized tests (Oliver, 1965). The present

engineering design graphics curriculum is not effectively teaching

spatial visualization to all students enrolled in such courses.

The glass box method of teaching spatial visualization has

become a monolithic standard of the 20th century. Transformational

leadership, as described by Bennis and Nanus (1985), in the form of

this study, has shown there may be another way.

The Scope and Limits of the Study

The scope of the study was limited to available engineering

graphics students enrolled during the Winter quarter 1991-1992 at

Ferris State University, Big Rapids, Michigan. These students can­

not be considered representative of all engineering and technology

students nationwide. Therefore, results of this study should not be

routinely generalized to other academic settings. Also, the pos­

sible effects of facilities, hour of the day, and specific technical

major were not researched.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER II

RELEVANT LITERATURE

An evaluative study such as this is designed to assess the

worth of one instructional strategy over another when individual

learner cognitive differences are known. Therefore, comparative

studies that used two or more instructional methods in the teaching

of spatial visualization were reviewed fir s t. This was followed by

a review of studies that examined individual cognitive differences

as they related to spatial visualization knowledge as demonstrated

by achievement in multiview orthographic projection. Finally,

several underlying psychological constructs that affect the acquisi­

tion of spatial visualization knowledge were reviewed in light of

two instructional methodologies being used in this study ( i.e .,

glass box and bowl).

Comparative Instructional Methods

Vander Wall (1991) did a comparative study on the effectiveness

and influence of required supplemental video teaching upon visuali­

zation proficiency among other items. Six random class sections of

college level engineering graphics were selected to participate in a

one semester research project. Three classes were required to view

30 mini-video-cassettes which ranged from 9 to 25 minutes in length

each. Each video was a review of course material covered in class.

9

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Three classes were denied access to the videos.

A comparison of the visual proficiency of the two groups being

studied required a pre- and postvisualization test. All tests were

scored in total points and points were received for the number of

lines successfully drawn in each of several incomplete orthographic

projection problems. Group means were calculated for individuals

and for each class based on the pre- and postvisualization test

scores. £ values and significance levels were calculated for all

comparisons with no statistically significant differences being

found between individuals or within and among the groups.

Laws (1986) conducted an experiment to test the effects of

using three-dimensional models in a competency based format for

teaching drafting in college. Four intact mechanical drawing

classes (86 students total) were the subjects of this experiment.

Two groups used three-dimensional models to aid them in the visuali­

zation required to complete 10 competencies. The other two groups

were not permitted to use models. The time required to complete

each competency correctly was recorded. Analysis of variance tests

of significance were used. Time to mastery was significantly faster

for the two groups using three-dimensional models. Thereby, demon­

strating that the use of models aided in the completion of spatial

visualization tasks in this study.

Batey (1986) studied the effects of training specificity on

gender differences as related to spatial ability. Due to a well-

documented male advantage in spatial ability, Batey hypothesized

that females would respond more favorably to specific training than

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. males; that is to say, females would make greater relative gains

than males. A total of 67 adolescents (43 males and 24 females)

were randomly split into three experimental groups. Group 1 re­

ceived no relevant orthographic training. Group 2 received nonspe­

cific training in orthographic projection, and Group 3 received

highly specific spatial training. Each group received 10 hours of

training over 2 weeks and was tested for gains in spatial ability 2

days following the training.

Statistical analysis of the data yielded significant main ef­

fects for training specificity ( jj < .012) and sex (jd < .038). In

addition, further comparison indicated that the specific training

condition was significantly more effective than either the non­

specific training condition or the control condition. The cell

means suggested that males benefited from both nonspecific and spe­

cific training, whereas females only benefited from specific train­

ing. This suggests that specific spatial training is the preferred

instructional condition for a mixed sex population.

Cooperative and individual learning activities were studied by

Lauderbach (1986) for their effect on performance in visualization

of multiview orthographic projection. The group under study was 69

fu ll- and part-time undergraduate industrial arts education majors

enrolled in three sections of engineering graphics.

All students were given the Differential Aptitude Test-Spatial

Relations (DAT-SR, Bennett, Seashore, & Wesman, 1972) to determine

their spatial ability. Those students scoring above the mean were

identified as high visualizers, and those scoring below the mean

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. were considered low visualizers. Within intact classes individuals

were randomly assigned to five-member work groups and encouraged to

work together, while others were left to work individually. After

15 hours of orthographic projection training, all students were

posttested for visualization ability. The results showed no signif­

icant difference in posttest scores for individual learners when

compared to cooperative work groups. In addition, there was no

difference in the high and low visual izers working alone when com­

pared to high and low visualizers found in cooperative work groups.

This would indicate that cooperative learning activities do not

affect the visualization performance on orthographic projections

when compared to individual work.

Schotta (1984) researched the effect of selected instruction in

tactual-visual perception and idea sketching on visual imagery abil­

ity. A total of 102 industrial arts majors enrolled in basic engi­

neering graphics were randomly assigned into one of four groups.

Group 1 was administered tactual-visual instruction. Group 2 re­

ceived tactual-visual instruction plus idea sketching. Group 3

received only idea sketching, and the fourth group received neither

form of specialized treatment.

Tactual-visual instruction involved the touching of several

wooden blocks of various shapes one at a time while the blocks were

hidden from view. Later each subject was asked to identify the

block previously touched from several pictures of drawn blocks;

there was four distracter shapes in each set. In idea sketching,

advocated by McKim (1980a, 1980b), the wooden blocks were viewed and

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. then sketched.

Visual imagery ab ility was measured by the DAT-SR. Hypotheses

were tested at the .05 level of significance using a single classi­

fication analysis of variance. No significant difference in the

visual imagery ab ility was found among any of the four treatment

groups. From this study it was concluded that neither tactual-

visual perception nor idea sketching affected visual imagery abil­

ity.

Groom (1982) wanted to determine the efficiency of using com­

puter graphics as a tool to teach basic engineering design graphics

at the college level. The course included five units of instruc­

tion, one of which was orthographic projection.

To test his hypothesis, Groom (1982) used two classes of begin­

ning graphics students. One group was required to complete all

assignments using manual drafting methods. The second group was

required to do the firs t assignment in each unit using manual draft­

ing methods, followed by the use of interactive computer graphics

for all remaining assignments.

The treatment was analyzed in terms of three major measure­

ments. The firs t measurement related to success on five quizzes;

the second on scores on the departmental comprehensive final; and

third, knowledge of computer graphics. There was no significant

difference between the groups on their quizzes. However, scores on

the final exam and computer graphics showed a significant inter­

action in favor of the use of computer graphics.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The computer graphics treatment group finished assignments much

faster (an average of 5 minutes versus 42) than the manual group,

thus allowing for time to teach computer graphics.

The effects of color versus monochrome cueing on drafting

visualization were the subject of a study by Gunter (1981). The

research investigated the impact that the use of color cueing (i.e .,

hinting) may have on the acquisition of visualization principles,

concepts, and abilities in beginning drafting students.

A total of 67 seventh-grade students enrolled in a beginning

drafting class was randomly split into two groups. Each student

was given a series of standard ( i.e ., DAT) and researcher developed

tests on spatial relations, orthographic projection, and visualiza­

tion. Next, each group was presented a four unit slide and tape

presentation. One group received the presentations in black and

white, while the experimental group received color presentations.

Posttests were given to all subjects of the study.

An analysis of the data showed no significant difference in

visualization ability achievement between the control and treatment

groups. Given the results of this study, it would appear that color

presentations offer no particular advantage over black and white

presentations when orthographic projection achievement is the de­

sired result.

Groves (1970) developed a research study designed to determine

whether background music would have any effect on learning achieve­

ment in university level engineering graphics classes. A second aim

of the study was to see if the presence of background music would

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. cause a change in the amount of noise generated by students during

class.

Six sections of freshmen engineering graphics containing a

total of 222 students were studied. Three classes received back­

ground music and three did not. Incidents of noise exceeding 60

decibels were recorded in all groups. Learning achievement was

measured by pooling jt tests on students' grades on daily assign­

ments, quizzes, number of layouts completed, and the final exam.

The with-music groups were quieter during 14 weeks of the 15

week semester. Also they had IQ% fewer incidents of noise per hour.

This was found to be significant at the .20 level of confidence.

The with-music groups also made higher semester grades, which was

again significant at the .20 level of confidence.

The researcher in this study concluded that background music

caused a measurable improvement in the achievement of students in

engineering graphics classes.

Campbell (1969) compared the traditional lecture-demonstration

method of teaching mechanical drawing to programmed instruction

units on selected elements of orthographic projection. This was

done to determine the effect these two methods would have on the

ability of pupils to visualize spatial relations.

A total of 188 high school students was involved in the study.

The Differential Aptitude Test of Space Relations (DAT-SR) was given

as a pretest and to test for equal groups. Individual classes were

left intact. One half of the groups received instruction in a tra ­

ditional lecture-demonstration format while the remaining groups

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. also received programmed instructional materials.

The DAT-SR was given to all subjects/groups as a posttest to

determine their gains in ability to visualize spatial relations. At

the .05 level of confidence there was no significant difference

between the achievement of the control and experimental groups.

Because several teachers were involved in this study, the re­

searcher also analyzed the achievement data in light of the experi­

ence level of the teacher for each class. Again, no significant

difference was found at the .05 level.

Sullivan (1964) conducted an experimental study of the effec­

tiveness of two methods of teaching orthographic projection in terms

of retention and transfer. Both methods are forms of orthographic

projection. One method began with multiview orthographic projection

followed by isometric drawing. The second method began with axonom-

etry which was then correlated to multiview projection.

Ninety-six 8th-grade boys with no previous experience in ortho­

graphic projection were the subjects of this study. They were left

in six intact groups of 16. One half of the groups received in­

struction beginning with orthographic projection. The remaining

groups received instruction beginning with axonometry.

At the conclusion of the instruction, researcher designed tests

for both axonometry and orthographic projection were given. Tests

were given to all subjects again 1 week and 24 days after the con­

clusion of instruction. In every case, groups exposed to axonometry

firs t out-performed those being introduced to orthographic projec­

tion first.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A logical conclusion would be that axonometry should be taught

prior to orthographic projection, not after it.

Summary of Research on Instructional Methods

From the research it is clear that certain instructional meth­

ods appear to improve the learner's ability to spatially visualize

three dimensional information and apply it to multiview orthographic

projection. Variables that were shown to positively affect spatial

visualization development were the use of models, specific training,

manual drafting plus interactive computer graphics, background

music, and exposure to axonometry. These seemingly unrelated varia­

bles can be linked to right brain cognitive functions. When the

right brain cognitive functions are engaged, spatial abilities are

enhanced (Edwards, 1989). The variables of using models, specific

training, and interactive computer graphics are concrete and charac­

terized by immediate experience of actual things or events. Teach­

ing graphics with axonometry is a holistic method of showing objects

on a two dimensional medium. The variable of music ties to the

right brain cognitive functions of nonverbal and nontemporal

thought.

Other variables shown through research to have no significant

effect on spatial visualization development are videos, cooperative

learning, tactual use of models, color, and teacher experience.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Studies of Individual Cognitive Difference

Baird (1989) tried to correlate a visual-haptic cognitive style

and a student's ab ility to solve orthographic projection problems

using computer aided drafting. Briefly stated, a visual-haptic

cognitive style relies on a sense of touch to aid in the process of

visualization.

A total of 136 college students enrolled in 11 sections of

beginning drafting were the subjects of this study. The Successive

Perceptions Test I was used to separate the sample population into

two groups, visual and nonvisual. Groups were further subdivided

into those with and without prior drafting experience. Six sections

received training using computer assisted drafting (CAD), while five

sections received training using manual tools.

Drawing grades and unit exams were used as indicators of abil­

ity to solve orthographic projection problems. The only correlation

found was between prior drafting experience and achievement.

One could question whether or not using CAD is more haptic than

using manual drafting tools. Also, the visual and nonvisual catego­

ries may not have properly isolated the visual-haptic cognitive

style.

Lajoie (1986) compared strategies used by experts and novices

to solve orthographic projection problems. Based upon her findings,

she developed a computerized tutor where students could explore

spatial relations actively, make predictions, and test their hypoth­

eses.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Lajoie (1986) found that experts and novices scoring 100% on a

pretest of multiview orthographic projection problems used a con­

structive strategy, while those doing poorly on this task used an

analytic strategy. The orthographic projection tutor (OPT) provided

analytic individuals with transition rules describing how points,

lines, and planes shown in two-dimensions appear on a three-dimen­

sional object. The research indicated that some individuals could

be taught the constructive methodology while others, using the OPT,

simply could not.

Kelley (1985) completed a study that used the Group Embedded

Figures Test and the Hidden Figures Test as predictors of success in

engineering graphics as indicated by the final letter grade in the

course. These tests are used to indicate field independence and/or

fle x ib ility of closure cognitive styles.

A total of 166 students enrolled in 10 sections of engineering

graphics were the subjects in this study. This included 133 males

and 33 females all of whom took the Group Embedded Figures Test

(GEFT) and the Hidden Figures Test (CF-1) at the beginning of the

semester.

Multivariate (jl = .321) and bivariate correlation coefficients

(GEFT _r = .302 and CF-1 £ = .280) provide an indication that these

tests could be used as valid predictors of success in engineering

graphics.

In another study, Dahl (1984), the GEFT was used to indicate

field dependence/independence in students enrolled in four sections

of engineering graphics. Because it is theorized that field

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dependent individuals have d ifficu lty imposing structure on an un­

organized perceptual fie ld , Dahl created a structured learning envi­

ronment in an effort to eliminate achievement differences in field

dependent and independent students.

Structure was provided in the form of a computer aided instruc­

tional (CAI) package that involved d rill and practice in ortho­

graphic projection. Field dependent students completing the d rill

and practice CAI package showed no significant gains in achievement

over students with the same cognitive learning style not using CAI.

In another study involving the field independent/dependent

cognitive styles, Moore (1982), tried to predict student success in

engineering graphics by employing the Group Embedded Figures Test

(GEFT).

The GEFT was given to 80 students enrolled in four sections of

engineering graphics and it was found to significantly correlate

with success as measured by the final course grade. The Pearson

product-moment correlation coefficients found for the final grade

and the GEFT relationship was £ = .485; jd < .001. This study, as

did the Kelley (1985) study, indicates that the GEFT has validity as

a predictor of success in engineering graphics.

Wilson (1982/1983) made a study of hemispheric dominance and

student performance in several engineering graphics courses. A

variety of characteristics were considered in assigning hemispheric

dominance to each subject. A portfolio of each student's drawings

was rated by three independent consulting experts and an average of

the three ratings was compared to hemispheric dominance. The data

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21

showed that right-brain students performed better than left-brain

students.

Summary of Research on Cognitive Characteristics

From the research it is evident that individuals who are right-

brain dominant, field independent, and use a constructive strategy

in solving orthographic projection problems will do well in the

study of college level engineering graphics. However, not all indi­

viduals possess or display a predisposition to these specific cogni­

tive characteristics. Therefore, any planned instructional method

which is expected to improve learner performance in spatial visuali­

zation tasks must tap into certain underlying psychological con­

structs .

The following section is a review of existing knowledge about

psychological constructs and cognitive characteristics which may be

exploited in the teaching of multiview orthographic projection.

Psychological Constructs

Several underlying psychological constructs that affect spatial

visualization development will be discussed in this section. First,

the visual system is fin ite and possesses temporal resolving power

(Neisser, 1967). This time limited resolving power gives the

teacher of multiview orthographic projection an unknown length of

time to demonstrate any spatial visualization technique. Therefore,

it would follow that quickly executed visualization demonstrations

will be followed visually, while lengthy demonstrations may fa ll

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. outside of the visual systems' temporal resolving power.

This time related visual resolving power can be thought of as

an individual's attention span. This visual attention can often be

observed in individuals with their fixation of gaze or visual track­

ing (Randhawa & Coffman, 1978). A visualization demonstration tech­

nique that permits visual tracking will hold an individual's atten­

tion in a way that a discontinuous demonstration will not. The

human visual attention span has also been measured using the elec­

troencephalogram (EEG). The EEG measures cortical processes ( i.e .,

action within the cerebral cortex), which are recorded as alpha

rhythms. These alpha rhythms are shown to be suppressed during

attention to visual stimuli (Randhawa & Coffman, 1978). This alpha

suppression declines with repeated stimulation. Therefore, a multi­

stimuli demonstration will be less effective ( i.e ., more d iffic u lt

to follow) than one employing a single stimulus.

Second, the human visual field during forward locomotion is a

hemispherical surface around the head. This continuous movement

through space creates corresponding retinal images that are best

described as flowing according to certain systematic rules (Haber &

Hershenson, 1973). These rules place the human visual system at the

center of rotation.

Finally, several studies of hemispheric dominance have v a li­

dated that spatial perception resides on the right side of the brain

(Edwards, 1989). Right brain dominant individuals also tend to take

a holistic view of the perceptual field. This holistic view of

patterns in two-dimensional space is in keeping with Gestaltic

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. concepts of articulation and differentiation which is insight, de­

fined as reorganization of the perceptual field (Gibson, 1969).

With both right brain dominance and Gestalt psychology, the holistic

view of visual imagery tends to improve the individual's ability to

solve complex visualization problems.

Summary of Research on Psychological Constructs

Instructional methods which capitalize on a human being's lim­

ited attention span, natural system of viewing, and desire to see the

big picture have been found to enhance an individual's spatial visu­

alization ability. As previously discussed (see Summary of Research

on Instructional Methods), the use of models and exposure to axonom­

etry improved spatial visualization ability. Both of these tech­

niques tie into the human's natural system of viewing. Interactive

computer graphics, which was also found to improve one's spatial

visualization ability tends to command the attention of the learner.

Also, as discussed in the section covering research on cogni­

tive characteristics, right brain dominant individuals were found to

do well in engineering graphics as were field independent students.

Both of these characteristies are related to the Gestaltic psycho­

logical constructs of articulation and differentiation (i.e ., reor­

ganization of the perceptual field into a holistic view).

The Hinged Glass Box

For the past 100 years, the hinged glass box has been used to

teach multiview orthographic projection. With this method an object

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. is placed inside of a real or imaginary hinged glass box (see Figure

1). After the object has been projected onto all sides of the glass

box, it is unfolded into a single two-dimensional surface showing

each view in relationship to one another. This method of teaching

multiview orthographic projection can be found in every basic draft­

ing text and a model of the hinged glass box will be found in most

drafting laboratories.

Although popular, the hinged glass box method requires either

very sophisticated mental rotation and projection of the object onto

the sides of the box or it requires physical movement around the

encased object. This method of teaching orthographic projection

does not follow the underlying psychological constructs which have

been found to facilitate spatial visualization.

The Bowl/Hemisphere

The bowl/hemisphere is a l it t l e known and unconventional method

of imagery used to teach multiview orthographic projection. With

this method, an object is placed in the middle of a bowl or hemi­

spheric shape (see Figure 2). The front view of the object is

viewed by looking directly into the bowl from above. Adjacent views

are developed by sliding the object along the surface of the bowl

until another side of the object is fu lly exposed.

Several underlying psychological constructs that affect spatial

visualization development seem to indicate that the bowl/hemisphere

instructional method of teaching multiview orthographic projection

will be superior to that of the hinged glass box method. The bowl

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25

THE GLASS BOX

FRONT VIEW

THE GLASS BOX UNFOLDED

Figure 1. The Hinged Glass Box.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. BOWL/HEMISPHERE IMAGERY

FRONT VIEW

ORTHOGRAPHIC VIEWS DEVELOPED

Figure 2. The Bowl/Hemisphere.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission technique can be executed in less time than the glass box because

there are fewer steps in the bowl method ( i.e ., only the object is

moved in the bowl method; whereas, the object must be projected and

the glass box unfolded in the traditional method). This means that

some individuals who were unable to follow the glass box method due

to loss of attention may be able to stay with the shorter bowl dem­

onstration.

The bowl method also focuses attention on an object placed in

the center of a hemisphere and this method, unlike the glass box,

permits the object to be tracked as adjacent views are developed.

The bowl method, which places a hemisphere in front of the

learner, is in keeping with the human centered visual system. The

glass box method runs counter to a lifetime of visualization, while

the bowl method mirrors the natural system. The bowl method of

spatial visualization permits a singular and holistic viewing of a

multiview orthographic projection; the glass box method does not.

The bowl/hemisphere method of teaching multiview orthographic pro­

jection provides the graphics educator and student a specific and

positive relationship to each of the underlying psychological con­

structs which have been found to facilitate spatial visualization.

Hypotheses

As previously stated in Chapter I, the purpose of this study

was to compare the effectiveness of one instructional method of

teaching multiview orthographic projection versus another ( i.e ., the

glass box vs. the bowl/hemisphere). The review of related

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. psychological literature indicated that bowl/hemisphere imagery may

be superior to glass box imagery when teaching spatial visualization

in the form of multiview orthographic projection. Therefore, the

following primary research hypotheses (numbers 1-4) were developed,

along subject visualization ability lines, and tested.

The secondary research hypotheses (numbers 5-7) were also de­

veloped and tested. Hypothesis 5 served to compare spatial visuali­

zation learning gains achieved by the control group, without benefit

of an instructional treatment (i.e., the pretest/posttest effect),

with gains achieved by either of the two instructional treatment

groups. Hypotheses 6 and 7 were created to compare visualization

achievement gains by aptitude level within the two instructional

treatment groups. For all seven hypotheses, ability partitioning

allowed for an examination of posttreatment gains in individuals at

the extremes of the visualization ab ility spectrum.

Primary Research Hypotheses

Hypothesis 1: The visualization achievement gain of low visu­

al izers in treatment Group 1 (the glass box) will not be as high as

the achievement gain of low visualizers in treatment Group 2 (the

bowl).

Hypothesis 2: The visualization achievement gain of middle low

visualizers in treatment Group 1 (the glass box) will not be as high

as the achievement gain of middle low visualizers in treatment Group

2 (the bowl).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Hypothesis 3: The visualization achievement gain of middle

high visualizers in treatment Group 1 (the glass box) will not be as

high as the achievement gain of middle high visualizers in treatment

Group 2 (the bowl).

Hypothesis 4: The visualization achievement gain of high

visualizers in treatment Group 1 (the glass box) will not be as high

as the achievement gain of high visualizers in treatment Group 2

(the bowl).

Secondary Research Hypotheses

Hypothesis 5: The average spatial visualization achievement

gain of Group 3 will not be as high as the gains recorded by either

Groups 1 or 2 as measured by the posttest.

Hypothesis 6: The posttreatment gain scores of the four apti­

tude levels within Group 1 (the hinged glass box) will be equal.

Hypothesis 7; The posttreatment gain scores of the four apti­

tude levels within Group 2 (the bowl/hemisphere) will be equal.

A Final Comment

This literature review demonstrates that spatial visualization

and orthographic principles have been the concern of researchers for

some time. Much is known; however, other methods of teaching visu­

alization must be researched. The inquiry described in research

study represents a contribution to known instructional methodologies

and the literature.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER I I I

RESEARCH DESIGN AND METHODOLOGY

The following research procedures were used to evaluate student

spatial visualization ability as it related to multiview ortho­

graphic projection achievement in basic engineering graphics at

Ferris State University, Big Rapids, Michigan, through the testing

of the seven research hypotheses outlined in Chapter II.

Population

The population from which subjects were selected for this study

was made up of freshmen and sophomores majoring in technical fields

and enrolled at Ferris State University during the Winter quarter of

1991/1992. Ninety-two predominantly male volunteers enrolled in

basic engineering graphics were the subjects of this study.

Research Design

The design of this study provided a framework for evaluation

and gave validity to the findings. Ninety-two subjects were re­

cruited from a total of 95 students enrolled in two basic engineer­

ing graphics courses. To insure consistency and fairness in the

subject selection procedure, a formal recruitment script was read to

the students in each graphics course (see Appendix B). Due to the

required nature of these graphics courses for many students,

30

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. participation in the study was on a voluntary basis. Assurances

about the voluntary nature of the study and the confidentiality of

all participants were made in a consent form (Appendix C). Each

volunteer subject read, signed, and dated a separate consent form

indicating their willingness to participate in the study. Those

students not wishing to participate in the study were asked to sign

a made-up name or simply leave the consent form blank.

Pretest for Spatial Visualization Ability

All subjects involved in the study were firs t given the Differ­

ential Aptitude Test-Spatial Relations-Form T (DAT-SR-T, Bennett et

al., 1972) to determine their current spatial visualization ability.

In other studies of this type by Lauderbach in 1986, Gunter in 1981,

and Campbell in 1969, the DAT-SR was used for the same purpose. The

DAT-SR-T is a 60-item test published by the Psychological Corpora­

tion. Instruction for administration of the 25 minute DAT-SR-T and

sample items are shown in Appendix D.

The DAT-SR-T has a re lia b ility coefficient of .95 and .94 for

12th grade boys and girls, respectively (Bennett, Seashore, & Wes-

man, 1974). For 11th grade students taking drafting, the DAT-SR-T

has a predictive validity coefficient of .51-.57 to the course grade

(Bennett et a l., 1974). The DAT-SR-T has also been correlated to

the fu ll range of subjects tested by the Iowa Tests of Educational

Development, the Metropolitan Achievement, the Scholastic Aptitude

Test, and the American College Testing Program's ACT (Bennett et

al., 1974). To date, no adult validity, reliability, or norm

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32

information is available from the Psychological Corporation on the

DAT-SR-T. However, the literature gives broad and wide ranging

support for the use of this instrument in spatial visualization

research on college age populations.

From the results of the scores attained on the DAT-SR-T, a

frequency distribution was created for one large class of 62 sub­

jects including cumulative frequencies and cumulative percentages

(see Table 1). The cumulative percentages were used to divide this

group of subjects into quartiles. Subjects found in these quartiles

were categorized as: low visualizers, middle low visualizers, mid­

dle high visualizers, or high visualizers. A stratified random

sampling technique was used to split the class of 62 subjects into

two equal treatment groups of 31, labeled Groups 1 and 2 (see Table

2).

Table 1

Frequency Distribution of the DAT-SR-T Scores

Cum. Spatial visual Array Freq. Freq. % C% ab ility level

17 1 1 1.6 1.6 Low

18 1 2 1.6 3.2 Low

21 2 4 3.2 6.5 Low

22 2 6 3.2 9.7 Low

23 1 7 1.6 11.3 Low

24 1 8 1.6 12.9 Low

32 1 9 1.6 14.5 Low

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33

Table 1— Continued

Cum. Spatial visual Array Freq. Freq. % C% ab ility level

34 3 12 4.8 19.4 Low

35 3 15 4.8 24.2 Low

36 2 17 3.2 27.4 Middle low

37 1 18 1.6 29.0 Middle low

38 5 23 8.1 37.1 Middle low

39 1 24 1.6 38.7 Middle low

40 5 29 8.1 46.8 Middle low

41 3 32 4.8 51.6 Middle high

42 1 33 1.6 53.2 Middle high

43 1 34 1.6 54.8 Middle high

44 6 40 9.7 64.5 Middle high

45 4 44 6.5 71.0 Middle high

46 2 46 3.2 74.2 Middle high

47 1 47 1.6 75.8 High

48 2 49 3.2 79.0 High

49 1 50 1.6 80.6 High

50 2 52 3.2 83.9 High

51 5 57 8.1 92.0 High

52 1 58 1.6 93.6 High

55 2 60 3.2 96.8 High

57 2 62 3.2 100.0 High

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 34

Table 2

DAT-SR-T Raw Score Test Results by Group

Group 1 Group 2 Group 3 Subject DAT-SR-T DAT-SR-T DAT-SR-T score score score

1 17 18 19

2 21 21 22

3 22 22 24

4 23 24 34

5 32 34 35

6 34 35 36

7 34 35 37

8 35 36 37

9 36 38 38

10 37 38 38

11 38 38 38

12 38 40 39

13 39 40 39

14 40 40 39

15 40 41 39

16 41 41 40

17 42 43 40

18 44 44 40

19 44 44 40

20 44 44 42

21 45 45 44

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35

Table 2—Continued

Group 1 Group 2 Group 3 Subject DAT-SR-T DAT-SR-T DAT-SR-T score score score

22 45 45 46

23 46 46 46

24 47 48 47

25 48 49 48

26 50 50 48

27 51 51 49

28 51 51 52

29 51 55 55

30 52 55 57

31 57 57 —

Totals 1,244 1,268 1,208

Note. Group 1 mean = 40.13; = 9.4; u = 31. Group 2 mean = 40.90; s = 9.8; ji = 31. Group 3 mean = 40.27; _s = 8.6; n^ = 30.

Another intact class of 30 subjects was selected to be the

control group and subsequently received no instructional treatment

during the time of this study. The DAT-SR-T was also given to this

group and the resultant scores were later used to insure the statis­

tical equality of spatial visualization ability among all three

groups (see Table 2 and Chapter IV, respectively).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Pretest for Orthographic Projection Knowledge

The Western Michigan University Diagnostic/Achievement Quiz,

Part 3, Spatial Perception (Nowak, Walter, Vander Ark, & Henry,

1991) was used as a second pretest. This pretest is a 12-item in­

strument that specifically tests spatial visualization as demon­

strated through orthographic projection. This instrument has been

given to several thousand students and the items are statistically

arranged from the simple to complex. Instructions for administra­

tion of this test and sample items are shown in Appendix E. The

items contained in the test were developed and reviewed by subject

matter experts, thereby insuring the content validity of this in­

strument. Also, the level of complexity found in the test was suf­

ficient to create a necessary and useful spread in demonstrated

learner development.

Individual achievement on this second pretest was used as a

baseline from which posttreatment gains were measured (see Table 3).

Also, for purposes of future reference in related research, a Pear­

son r. correlation coefficient was calculated for the two pretests

using the raw score formula and the data tables found in Appendix F.

A moderate positive correlation of .50 was found between the pre­

tests and is discussed further in Chapter IV.

Design of Treatment

Following all pretesting, the instructional methodology treat­

ment ( i.e ., the independent variable) was administered separately to

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37

Table 3

Comparison Table of DAT-SR-T Pretest Scores and Orthographic Spatial Perception Pretest Scores by Individual Subject and Group

DAT-SR-T pretest score/orthographic pretest score

Subject Group I Group 2 Group 3

1 17/3 18/3 19/0

2 21/3 21/5 22/3

3 22/1 22/0 24/4

4 23/5 24/3 34/2

5 32/2 34/2 35/2

6 34/4 35/1 36/3

7 34/4 35/3 37/7

8 35/1 36/5 37/3

9 36/2 38/2 38/4

10 37/5 38/4 38/2

11 38/3 38/3 38/7

12 38/4 40/3 39/6

13 39/3 40/6 39/3

14 40/3 40/3 39/4

15 40/2 41/6 39/3

16 41/3 41/5 40/2

17 42/8 43/1 40/3

18 44/3 44/3 40/4

19 44/5 44/5 40/2

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38

Table 3--Continued

DAT-SR-T pretest score/orthographic pretest score

Subject Group 1 Group 2 Group 3

20 44/6 44/4 42/3

21 45/8 45/5 44/5

22 45/8 45/5 46/5

23 46/5 46/6 46/4

24 47/5 48/3 47/5

25 48/7 49/3 48/3

26 50/10 50/6 48/3

27 51/4 51/6 49/4

28 51/4 51/5 52/8

29 51/4 55/4 55/4

30 52/5 55/8 57/6

31 57/9 57/7 —

Note. DAT-SR-T pretest has 60 items and the Orthographic Spatial Perception pretest has 12 items.

the split Groups 1 and 2 during 2 hours each of specific and formal

lecture. This 2 -hour time frame is specified on the Ferris State

University's official course outline as being required for the in­

troduction and use of spatial visualization imaging.

Group 1 received instruction in orthographic principles using

the hinged glass box imagery. Group 2 received instruction in or­

thographic principles using the bowl/hemisphere imagery. Examples,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 39

time, and topics covered during the instructional treatment were

identical except for the spatial rotation imagery used. Group 3,

the control group, received no instruction in orthographic princi­

ples during the time of this study.

The Posttest

Following the instructional treatment given to Groups 1 and 2

as well as the absence of an instructional treatment for Group 3,

all subjects were given a posttest. The posttest was again the 12-

item spatial perception instrument previously administered as the

second pretest (see Appendix E). Scores on the posttest were used

to record gains in multiview orthographic projection type spatial

visualization development ( i.e ., the dependent variable) in individ­

uals, categories, and groups. These data are displayed by group in

Chapter IV.

Insuring Subject Confidentiality

To insure the confidentiality of the subjects who participated

in this research study, the following procedure was followed:

First, a master f ile was created listing those volunteers who signed

consent forms by class. These were made in alphabetical order.

Second, on the reverse side, in the lower right hand corner of

each of the three different blank test answer sheets, a coded number

was written. This number was a 5-digit number such as 60427 or

31562. Reading left to right, digits 1, 3, and 5 are random numbers

having no meaning. Digits 2 and 4 indicate a position of a name on

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the alphabetical master lis t ( i.e ., 02 = 2nd position from the top,

and 16 = 16th position from the top). These numbers ( i.e ., digits

1, 3, and 5) were different for the pretest and posttest answer

sheets.

Third, to further mask any possible detection of a pattern, the

original master alpha lists were randomized two times creating two

new ordered lists of names for use in passing out the test booklets

and coded blank answer sheets.

Both master alphabetical name lists and all scored answer

sheets were kept in separate locations under lock and key. Once the

last of three tests had been given, a new master lis t linking pre­

test and posttest scores was created without any reference to the

individual participants. And the original master alphabetical name

lists were destroyed, thereby insuring total subject confidential­

ity.

Threats to Validity

Whenever a pretest is given, a certain amount of learning takes

place simply through exposure to the test (Krathwohl, 1988). This

kind of pretest treatment interaction was accounted for in this

study by the use of a control group.

There is also a possibility that subjects from each of the two

instructional treatment groups conversed about the method by which

they were being taught orthographic principles. If this kind of

interaction was lengthy and widespread, contamination of the treat­

ment effect could occur. Due to the short duration between

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. pretesting and posttesting and the complexity of the instructional

treatment the probability of contamination seems remote.

To eliminate concerns about spatial visualization development

taking place through either psychomotor or time on task learning, no

laboratory assignments were made prior to the administering of the

posttest.

An Ethical Concern

Group 2 received a nontraditional approach to the visualization

process needed to understand multiview orthographic projection.

Because the treatment given to this group is not widely known or

accepted, Group 2 was also instructed in the glass box visualization

technique following the posttest. And Group 1 was shown the

bowl/hemispheric visualization technique.

Data Analysis

A complete record of raw data generated through pre- and post­

testing was made by subject, group, and spatial visualization abil­

ity level (see Appendix H). Appendix H was created via micro­

computer using the spreadsheet software package PC-CALC 3.0 (Button,

1985). This computer based record was then verified for accuracy

against original records. The microcomputer data were then trans­

lated into standard ASCII code for loading into a file on the Ferris

State University (Big Rapids, Michigan) mainframe computer. The

statistical package for the social sciences (SPSS, Inc., 1990) re­

lease 4.1 was then used for formal data analysis. However, prior to

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. analysis the data loaded into SPSS were again checked for accuracy

against both the microcomputer data (Appendix H) and original re­

cords.

Formal analysis began with a facilitatin g check for equality of

spatial visualization ability between all three groups participating

in the study using one-way analysis of variance (ANOVA). A _t test

for independent sample means was used to test each of the four pri­

mary research hypotheses. Measures on the dependent variable, spa­

tial visualization development, were treated as interval data. The

average spatial visualization achievement gain of Groups 1, 2, and 3

(Hypothesis 5) was analyzed using one-way ANOVA. Finally, post­

treatment gain scores for the four aptitude levels within Groups 1

and 2 (Hypotheses 6 and 7) were analyzed using one-way ANOVA. All

hypotheses were tested at the .05 level of significance.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER IV

FINDINGS

This study was designed to explore the effectiveness of one

instructional method versus another as it related to spatial visual­

ization and the teaching of multiview orthographic projection. In

this chapter the findings of the research study are reported. These

findings are based upon data collected through the research design

and methodology described in Chapter I I I .

Treatment effect data recorded as a result of posttreatment

gains ( i.e ., the dependent variable) for Groups 1 (box), 2 (bowl),

and 3 (control) are found in Tables 4, 5, and 6, respectively. Note

that subjects for which no posttest score was received have been

omitted from the data tables at this point.

Table 4

Group 1 (Hinged Glass Box Imagery) Treatment Effect Data by Aptitude Level

12-item 12-item Visualization Subject pretest posttest Gain ability score score category

1 - ---

2 3 3 0 Low

3 1 1 0 Low

4 5 4 -1 Low

43

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 44

Table 4--Continued

12-item 12-item Visualization Subject pretest posttest Gain abi1ity score score category

5 2 5 3 Low

6 4 6 2 Low

7 4 5 1 Low

8 1 4 3 Low

R = 7 20 28 8 = Subtotal

2.85 Avg. 4.00 Avg. 1.14 = Mean gain

9 2 5 3 Middle low

10 5 2 -3 Middle low

11 3 3 0 Middle low

12 4 2 -2 Middle low

13 3 6 3 Middle low

14 3 3 0 Middle low

15 2 7 5 Middle low

n = 7 22 28 6 = Subtotal

3.14 Avg. 4.00 Avg. 0.85 = Mean gain

16 3 5 2 Middle high

17 8 10 2 Middle high

18 3 5 2 Middle high

19 5 5 0 Middle high

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45

Table 4--Continued

12-item 12-item Visuali zation Subject pretest posttest Gain ability score score category

20 6 4 -2 Middle high

21 8 7 -1 Middle high

22 8 9 1 Middle high

23 5 8 3 Middle high

_n = 8 46 53 7 = Subtotal

5.75 Avg. 6.23 Avg. 0.875 = Mean gain

24 5 6 1 High

25 7 9 2 High

26 10 10 0 High

27 4 5 1 High

28 4 6 2 High

29 4 6 2 High

30 5 5 0 High

31 9 10 1 High 00 =1 II 48 57 9 = Subtotal

6.00 Avg. 7.13 Avg. 1.125 = Mean gain

n = 30 Total

Totals 136 166 30

Means 4.53 5.53 1.00

Std. dev. 2.30 2.40 1.78

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46

Table 5

Group 2 (Bowl/Hemisphere Imagery) Treatment Effect Data by Aptitude Level

12-item 12-item Visualization Subject pretest posttest Gain ab ility score score category

1 3 5 2 Low

2 5 6 1 Low

3 0 2 2 Low

4 3 4 1 Low

5 2 4 2 Low

6 1 2 1 Low

7 3 5 2 Low

_n = 7 17 28 11 = Subtotal

2.42 Avg. 4.00 Avg. 1.57 = Mean gain

8 5 4 -1 Middle low

9 2 4 2 Middle low

10 - - - -

11 3 4 1 Middle low

12 3 3 0 Middle low

13 6 6 0 Middle low

14 3 7 4 Middle low

£ = 6 22 28 6 = Subtotal

3.66 Avg. 4.66 Avg. 1.00 = Mean gain

15 6 2 -4 Middle high

16 5 4 -1 Middle high

17 1 5 4 Middle high

18 3 6 3 Middle high

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47

Table 5—Continued

12-item 12-item Visualization Subject pretest posttest Gain ability score score category

19 5 3 -2 Middle high

20 4 4 0 Middle high

21 - ---

22 5 6 1 Middle high

23 6 7 1 Middle high

n = 8 35 37 2 = Subtotal

4.38 Avg. 4.63 Avg. 0.25 = Mean gain

24 3 4 1 High

25 3 2 -1 High

26 6 5 -1 High

27 6 10 4 High

28 5 7 2 High

29 4 5 1 High

30 8 6 -2 High

31 7 9 2 High

n. = 8 42 48 6 = Subtotal

5.25 Avg. 6.00 Avg. 0.75 = Mean gain

_n = 29 Total

Totals = 116 141 25

Means = 4.00 4.86 0.86

Std. dev. = 1.91 1.95 1.86

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48

Table 6

Group 3 (No Instructional Treatment) Treatment Effect Data

12-item 12-item Subject pretest posttest Gain score score

1 0 4 4

2 3 2 -1

3 4 2 -2

4

5 2 4 2

6 3 6 3

7 7 5 -2

8 3 6 3

9 4 2 -2

10 2 3 1

11 7 5 - 2

12 6 4 -2

13 3 4 1

14 4 5 1

15 3 3 0

16 2 6 4

17 3 4 1

18 4 2 -2

19

20 3 5 2

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49

Table 6--Continued

12-item 12-item Subject pretest posttest Gain score score

21 5 2 -3

22 - --

23 4 4 0

24 5 7 2

25 3 3 0

26 3 6 3

27 4 2 -2

28 8 10 2

29 4 5 1

30 6 6 0

jn = 27 Totals = 105 117 12

Means = 3.89 4.33 0.44

Std. dev. = 1.76 1.90 2.08

A national norm mean score of 34.3 is reported by the Psycho-

logical Corporation for male 12th graders (N^ = >5,000) (Bennett et

a l., 1974). Group means in the range of 40-41 for college age engi­

neering and technology students seems plausible. Maturation and

specific interests found in the population being researched may

account for the differences in means. No adult norms exist. To

test for equality of spatial visualization aptitude between groups,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the data reported in Table 7 were analyzed using one-way ANOVA. The

results of this test are reported in Table 8.

Table 7

Summary of DAT-SR-T Pretest by Group

Mean Group a score SD

1 31 40.13 9.8

2 31 40.90 9.4

3 30 40.26 8.6

Table 8

.Analysis of Variance for Equality of Spatial Visualization Aptitude Between Groups 1, 2, and 3

Sum of Mean F F Source df squares squares ratio prob.

Between groups 2 10.5485 5.2742 .0597 .9421

The one-way ANOVA findings (_F probability = .9421) indicated

that the groups were not significantly different at the .05 level.

The equality of spatial visualization aptitude between groups facil­

itated the balance of the study.

A second pretest was administered to each group to evaluate its

present knowledge of multiview orthographic projection. This was a

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12-item test taken from the Western Michigan University Diag­

nostic/Achievement Quiz (Nowak et a l., 1991) (see Appendix E). A

summary of the results of this pretest is shown in Table 9.

Table 9

Summary of Orthographic Pretest Scores by Group

Mean Group a score SD

1 30 4.53 2.30

2 29 4.00 1.91

3 27 3.89 1.76

Information provided by the Western Michigan University Testing

and Evaluation Service (Nowak, 1991) indicated that a mean score of

4.2 was found in a random sampling of 100 firs t and second year

college males enrolled in technical programs. Again, mean scores

found in the groups listed in Table 9 are plausible. These scores

provided a baseline for the measurement of posttreatment gains.

For information purposes a Pearson _r correlation coefficient

of .50 was calculated between this orthographic pretest and the DAT-

SR-T using data found in Appendix F. This is a moderate positive

correlation that could be expected due to the use of spatial

visualization in both tests. The lack of a higher correlation is

discussed in Chapter V.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 52

Primary Research Hypotheses

Hypothesis 1 stated that the visualization achievement gain of

low visualizers in treatment Group 1 (the glass box) will not be as

high as the achievement gain of low visualizers in treatment Group 2

(the bowl/hemisphere). The average gain for each of these groups

was calculated by subtracting orthographic pretest scores from or­

thographic posttest scores. These mean gains were then compared in

a _t test for independent means (see Table 10).

The _t test yielded a calculated t_ value of -.68 with 12 degrees

of freedom. This was not significant at the .05 alpha level as the

critical value for a one-tailed test at the .05 level is -1.782.

Therefore, the directional Hypothesis 1 cannot be supported. How­

ever, the statistical information indicates the two instructional

Table 10

Comparisons of Posttreatment Gains of Low Aptitude Visualizers Between Instructional Treatments

Mean Calc. Critical Group gain SD t value df val ue of jt

1 7 1.1429 1.574 -.68 12 -1.782 2 7 1.5714 0.535

methods used are not significantly different. These findings are

further discussed in Chapter V.

Hypothesis 2 stated that the visualization achievement gain of

middle low visualizers in treatment Group 1 (the glass box) will not

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. be as high as the achievement gain of middle low visualizers in

treatment Group 2 (the bowl/hemisphere). The average gain for each

of these groups was calculated by subtracting orthographic pretest

scores from orthographic posttest scores. These mean gains were

then compared in a t_ test for independent means (see Table 11).

Table 11

Comparisons of Posttreatment Gains of Middle Low Aptitude Visualizers Between Instructional Treatments

Mean Calc. Critical Group N gain SD _t value df value of _t

1 7 0.8571 2.911 -.11 11 -1.796 2 6 1.0000 1.789

The jt test yielded a calculated jt value of -.11 with 11 degrees

of freedom. This was not significant at the .05 alpha level as the

critical value for a one-tailed test at the .05 level is -1.796.

Therefore, the directional Hypothesis 2 cannot be supported. How­

ever, the statistical information indicates the two instructional

methods used are not significantly different. These findings are

further discussed in Chapter V.

Hypothesis 3 stated that the visualization achievement gain of

middle high visualizers in treatment Group 1 (the glass box) will

not be as high as the achievement gain of middle high visualizers in

treatment Group 2 (the bowl/hemisphere). The average gain for each

of these groups was calculated by subtracting orthographic pretest

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54

scores from orthographic posttest scores. These mean gains were

then compared in a _t test for independent means (see Table 12).

Table 12

Comparisons of Posttreatment Gains of Middle High Aptitude Visualizers Between Instructional Treatments

Mean Calc, Critical Group N gain SD t value df value of t

1 8 0.8750 1.727 .57 14 1.761 2 8 0.2500 2.605

The _t test yielded a calculated t_ value of .57 with 14 degrees

of freedom. This was not significant at the .05 alpha level as the

critical value for a one-tailed test at the .05 level is 1.761.

Therefore, the directional Hypothesis 3 cannot be supported. How­

ever, the statistical information indicates the two instructional

methods used are not significantly different. These findings are

further discussed in Chapter V.

Hypothesis 4 stated that the visualization achievement gain of

high visualizers in treatment Group 1 (the glass box) will not be as

high as the achievement gain of high visualizers in treatment Group

2 (the bowl/hemisphere). The average gain for each of these groups

was calculated by subtracting orthographic pretest scores from or­

thographic posttest scores. These mean gains were then compared in

a t test for independent means (see Table 13).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 55

Table 13

Comparisons of Posttreatment Gains of High Aptitude Visualizers Between Instructional Treatments

Mean Calc. Critical Group N gain SD _t value df value of _t

1 8 1.1250 0.835 .49 14 1.761 2 8 0.7500 1.982

The t_ test yielded a calculated _t value of .49 with 14 degrees

of freedom. This was not significant at the .05 alpha level as the

critical value for a one-tailed test at the .05 level is 1.761.

Therefore, the directional Hypothesis 4 cannot be supported. How­

ever, the statistical information indicates the two instructional

methods used are not significantly different. These findings are

further discussed in Chapter V.

Secondary Research Hypotheses

Hypothesis 5 stated that the spatial visualization achievement

gain of Group 3 (no instruction) will not be as high as either in­

structional treatment Groups 1 or 2 as measured by pretest/posttest

gains. A global average gain for each of these groups was calcu­

lated by subtracting orthographic pretest scores from orthographic

posttest scores (see Table 14 for a summary).

To test for the statistical significance of the visualization

gain differences achieved between groups, the data summarized in

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56

Table 14 were analyzed using one-way ANOVA. The results of this

test are reported in Table 15.

Table 14

Posttreatment Visualization Gains Summary

Group £ Mean gain SD

1 30 1.00 1.78

2 29 0.86 1.86

3 27 0.44 2.08

Table 15

Analysis of Variance for Gain Score Comparisons Between Groups 1, 2, and 3

Sum of Mean F F Source df squares squares ratio prob.

Between groups 2 4.6874 2.3437 .6396 .5301

The one-way ANOVA findings (£ probability = .5301) indicated

that the gains achieved by treatment Groups 1 and 2 were not signif­

icantly different than those achieved by Group 3 at the .05 level.

This implies that learning by the control group, simply through

exposure to the pretest, is statistically equal to that of the two

groups who were taught using specific visualization imagery.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Hypothesis 6 stated that the posttreatment gain scores of the

four aptitude levels within Group 1 (the hinged glass box) will be

equal. The mean scores for Group 1 by aptitude level are displayed

in Table 16.

Table 16

Mean Scores by Aptitude Level for the Glass Box Treatment Group

Aptitude Pretest Posttest Mean level average average gain

Low 2.85 4.00 1.14

Middle low 3.14 4.00 0.85

Middle high 5.75 6.23 0.88

High 6.00 7.13 1.13

To test for equality of gains across aptitude levels within

Group 1, the data reported in Table 16 were analyzed using one-way

ANOVA. The results of this test are reported in Table 17.

Table 17

Analysis of Variance for Gain Score Comparisons Between Aptitude Levels Within Group 1

Sum of Mean F F Source df squares squares ratio prob.

Between levels 3 .5357 .1786 .0508 .9845

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 58

The one-way ANOVA findings (£ probability = .9845) indicated

that the gain scores between aptitude levels within Group 1 were not

significantly different at the .05 level.

Hypothesis 7 stated that the posttreatment gain scores of the

four aptitude levels within Group 2 (the bowl/hemisphere) will be

equal. The mean scores for Group 2 by aptitude level are displayed

in Table 18.

Table 18

Mean Scores by Aptitude Level for the Bowl/Hemisphere Treatment Group

Aptitude Pretest Posttest Mean level average average gain

Low 2.42 4.00 1.57

Middle low 3.66 4.66 1.00

Middle high 4.38 4.63 0.25

High 5.25 6.00 0.75

To test for equality of gains across aptitude levels within

Group 2, the data reported in Table 18 were analyzed using one-way

ANOVA. the results of this test are reported in Table 19.

The one-way ANOVA findings (£ probability = .6177) indicated

that the gain scores between aptitude levels within Group 2 were not

significantly different at the .05 level.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59

Table 19

Analysis of Variance for Gain Score Comparisons Between Aptitude Levels Within Group 2

Sum of Mean F F Source df squares squares ratio prob.

Between levels 3 6.7340 2.2447 .6063 .6177

Summary

This chapter focused on the statistical analysis of the data

collected and reported in Chapter I I I . Scores attained on each of

the pretests (DAT-SR-T and Orthographic) by the 92 subjects of the

study were in keeping with expectations based on test norms. And

the three groups used in this research began as statistical equals

in spatial visualization ability.

Each of the four primary research hypotheses predicting higher

orthographic projection achievement gains for those individuals

taught with the bowl/hemisphere imagery were rejected. They could

not be statistically supported, although within two visualization

aptitude levels (low and middle low) individuals averaged higher raw

score gains when taught with bowl/hemisphere imagery. And within

all four aptitude levels no statistically significant difference was

found in the orthographic projection knowledge gains of those indi­

viduals taught with glass box imagery and those taught with bowl/

hemisphere imagery.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The control group that received no instructional treatment

scored approximately one half of the gain in orthographic projection

knowledge found in the two groups receiving specific types of visu­

alization imagery. However, the control groups' gains were su ffi­

cient to be statistically equal to the two instructional treatment

groups. Therefore, Hypothesis 5 was also rejected.

Hypotheses 6 and 7 predicted that orthographic projection

knowledge gains across visualization aptitude levels and within

groups would be equal. Each of these hypotheses was statistically

supported. Questions raised by each of the findings revealed in

this chapter will be further discussed in Chapter V.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER V

CONCLUSIONS AND RECOMMENDATIONS

The modern engineering and technology bachelor of science cur­

riculum has been fixed at a fin ite 124 semester hours (ABET, 1989).

Concurrently, the seemingly exponential growth of engineering and

technical knowledge is being collapsed into the traditional four-

year B.S. degree program. Leaders in curriculum and instruction

( i.e ., engineering deans and department chairs) must examine the

value of all existing curricular content. For essential curriculum

material ( i.e ., multiview orthographic projection), more effective

and efficient delivery methods must be found. Therefore, the con­

struction of this research study began with a desire to prove that

the bowl/hemisphere method of teaching multi view orthographic pro­

jection would be more effective than the traditional glass box ap­

proach. As such, the independent variable manipulated in this study

was the instructional method used in teaching multiview orthographic

projection; and the dependent variable was the spatial visualization

development of students as demonstrated through their a b ility to

mentally solve complex multiview orthographic problems.

Seven specific research hypotheses were developed and tested,

thereby providing a framework for conclusions drawn in this chapter.

The four primary research hypotheses comparing the glass box method

of teaching spatial visualization to the bowl/hemisphere method were

61

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. tested using the t_ test for independent means.

The three secondary research hypotheses were also tested. The

firs t of these secondary hypotheses compared spatial visualization

gains of each of the two instructional treatment groups to the con­

tro l group and was tested using one-way analysis of variance

(ANOVA). The last two hypotheses, comparing spatial visualization

gains within treatment groups and across four aptitude levels, were

also tested using one-^ay ANOVA.

Pretesting for Spatial Visualization Ability

All 92 subjects who originally consented to participate in this

research study were given the Psychological Corporation's (1972)

Differential Aptitude Test, Space Relations, Form T (DAT-SR-T,

Bennett et al., 1972), as a pretest for spatial visualization abili­

ty. As a sample this group of 92 firs t and second year college

students scored a mean of 40.4 on the DAT-SR-T, with scores ranging

from a low of 17 to a high of 57 out of 60. No adult norms exist

for this test. However, norms for 12th grade boys (n_ = 5,000+) are

published by the Psychological Corporation (Bennett et a l., 1974).

These published norms indicate a score of 40.4 resides in the 65th

percentile, a score of 17 resides in the 10th percentile, and a

score of 57 resides in the 97th percentile for 12th grade boys

( i.e ., a score of 34 = 50th percentile).

The difference in spatial visualization ability between the

12th grade norms and the study sample scores can be accounted for

through two factors. First, when compared to 12th graders, a

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. minimum of from one to two years of mental maturation has occurred

in the sample group used in this study. Second, the sample used in

this study have all expressed an interest in engineering and tech­

nology through the selection of a technical college major. Consid­

ering these factors, the higher sample mean score was expected. In

addition, the range of scores achieved by the 92 research subjects

appears to be representative of the range that could be expected in

the general population. Therefore, on this one measure (i.e ., spa­

tial visualization a b ility ), the inference is that this sample group

is typical of those that would be found in other similar situations.

Mean scores achieved on the DAT-SR-T by the three treatment

groups used in this study were tested for equality using one-way

ANOVA (refer to Chapter IV). No statistical significant difference

was found between these groups at the .05 level. For purposes of

this research, the spatial visualization ab ility of the groups was

concluded to be equal. This equality makes posttreatment compari­

sons of spatial visualization ability valid.

Pretesting for Multiview Orthographic Projection Ability

A second pretest (the Western Michigan University Diagnostic/

Achievement Quiz: Part 3, Spatial Perception, Nowak, et a l., 1991)

was given to all subjects. This second 12-item pretest specifically

tested multiview orthographic projection knowledge. The scores

achieved on this pretest were used as a baseline from which to meas­

ure posttreatment gains in spatial visualization ability.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Complete data were collected on 86 subjects of the 92 who began

the study. The mean score achieved by the remaining 86 study par­

ticipants was 4.15 correct. Norm information was provided about

this 12-item test by Western Michigan University's Testing and Eval­

uation Service (Nowak et a l ., 1991). A norm mean score of 4.2 was

found using a random sample of 100 college age technical students

who previously took the test. Again, it was concluded that the

study participants were representative of firs t and second year

college students majoring in technical subjects.

A Pearson product-moment r. correlation coefficient was calcu­

lated between the two pretests. A .50 correlation coefficient was

found (refer to Chapter IV), indicating that there are some common

underlying psychological constructs being tested by both instru­

ments. However, this moderate positive correlation also indicated

differing psychological constructs were probed. These sim ilarities

and differences were expected due to the increased level of spatial

visualization sophistication required in the solving of multiview

orthographic projection problems.

Primary Research Hypotheses

Research on the underlying psychological constructs relating to

spatial visualization indicated that the bowl/hemisphere method of

teaching multiview orthographic projection may be superior to that

of the glass box method. Given this prediction, four primary re­

search hypotheses were developed and tested. Each of the four hy­

potheses were based upon the premise that spatial visualization

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. instruction using bowl/hemisphere imagery is superior to that which

uses glass box imagery. Four similar hypotheses were developed, one

to account for each of the following visualization aptitude levels:

low, middle low, middle high, and high (refer to Chapter I I I ) .

Group 1 received instruction in orthographic principles using

glass box imagery and Group 2 received similar instruction using

bowl/hemisphere imagery. Following this instruction, the 12-item

posttest was administered to each group and mean gains were computed

within groups for each aptitude level. Each primary research hy­

pothesis was then tested using these gain scores by aptitude level

in a jt test for independent means. Gains within each treatment

group were not found to be significantly different at the .05 level.

Therefore, each of the four primary directional research hypotheses

were rejected. Bowl/hemisphere imagery instruction was not found to

be better than glass box imagery instruction. However, the raw

score and _t test results served to show that bowl/hemisphere in­

struction yielded gains in visual knowledge that were roughly equal

to the gains yielded by the glass box instruction. From this infor­

mation, it can be concluded that the bowl/hemisphere method of visu­

alization is not, by its e lf, more effective than the glass box meth­

od. Yet, as a result of this study, the bowl/hemisphere method of

visualization cannot be considered of no value (see Recommendations

for Further Study).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 66

Secondary Research Hypotheses

Group 3 was used as a control group and received no formal

instruction in orthographic principles during the time of the study.

This group was used to account for knowledge gained through exposure

to the pretest, a phenomenon known as the pretest/posttest effect.

The firs t of the secondary research hypotheses ( i.e ., Hypothesis 5)

stated that the visualization achievement gains of the control group

would not equal the achievement gains of either of the two treatment

groups as measured by the posttest. Hypothesis 6 was tested using

one-way ANOVA. And although the raw score gains of the control

group were approximately one half that of either treatment group.

The gains of all three groups were not found to be significantly

different at the .05 level.

From the analysis of variance performed on the mean gains for

all three groups, it could be concluded that no visualization train­

ing was equal to 2 hours of very formal and intensive visualization

instruction ( i.e ., either the glass box or the bowl/hemisphere).

Although this conclusion may be statistically accurate, several

other explanations must be considered. First, raw score gains for

the two treatment groups were twice those of the control group;

however, 2 hours of visualization imagery may not have been enough

to yield gains that were statistically significant. By simply in­

creasing the visualization imagery training a given number of

minutes or hours, posttreatment gains may have been dramatically

increased. Second, the control group was an intact group of welding

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. majors. In the manual work performed by these welding students in

their laboratory courses, geometric shapes were routinely manipu­

lated and welded together. This type of manual work may have ac­

counted for some of the gain scored by this group on the posttest as

was the case in another study (Laws, 1986). Third, the control

group met at 8:00 a.m., while the treatment groups met at 3:00 p.m.

Therefore, the control group may have been more fresh and diligent

when they took the posttest.

Hypotheses 6 and 7 stated that the posttreatment gain scores of

the four aptitude levels within Groups 1 and 2 would be equal, re­

spectively. Both hypotheses were tested using one-way ANOVA. The

gain scores between aptitude levels within each group were found to

be not significantly different at the .05 level. This may be ex­

plained in the following way.

The 12-item posttest was statistically arranged from simple to

complex using data from thousands of students who previously at­

tempted answering each item in earlier versions of the instrument.

Therefore, gains made from the pretest to the posttest by lower

aptitude visualizers took place in the beginning items (i.e ., less

complex) of the instrument. Higher aptitude visualizers had to make

their gains among the ending items ( i.e ., more complex) of the in­

strument. In this way the construction of the test tended to even

out the gains across aptitude levels.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 68

Spatial Visualization Imagery

Leaders within the engineering education community have, for

some 100 plus years, tried to increase the effectiveness and e f fi­

ciency with which spatial visualization is taught and learned

(Booker, 1963). Successful representation of three-dimensional

objects on a two-dimensional medium requires spatial visualization

by the designer or drafter. Simply reading a blueprint requires re­

versing the visualization process from the two-dimensional paper

graphic to the three-dimensional object by all others. Spatial

visualization imagery, such as the bowl/hemisphere and glass box,

aids in this transition of the mind from two dimensional to three

dimensional and back to two dimensional. As previously stated in

Chapter I, Cronbach and Snow (1981) referred to these visualization

imagery aids as mental prostheses.This research study is further

evidence the spatial visualization imagery alone is not the answer.

As in the Lajoie (1986) study, lit t le proof was found in this study

that spatial visualization can be taught to all individuals and

transferred to a test. The time devoted to spatial visualization in

the modern engineering and technology curriculum may simply not be

enough. The higher levels of spatial visualization required of

engineering students and personnel may take years to fu lly develop,

as does reading. Yet, spatial visualization imagery provides the

learner with that firs t mental foundation upon which further psycho­

logical development is built.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69

Recommendations for Further Study

Given the findings of this study, it is clear that the effec­

tiveness issue of teaching spatial visualization was not resolved

through this research. However, the research on psychological con­

structs cited in Chapter II coupled with the findings discussed in

Chapter IV indicate that there is value in the bowl/hemisphere im­

agery. Leaders within the spatial visualization research and engi­

neering graphics education community may wish to conduct further

study on the use of bowl/hemisphere imagery. Therefore, the follow­

ing studies are proposed as they relate to spatial visualization and

leadership in the teaching of multiview orthographic projection.

1. Repeat this study with increased spatial visualization

lecture time. This study would find out if visualization imagery

alone can at some point create significant learning gains. As noted

by Raudebaugh (1988), educators are today typically teaching spatial

visualization principles in one fifth of the time they did 30 years

ago. Also, the visual systems temporal resolving power, as identi­

fied by Randhawa and Coffman (1978), may require increased demon­

stration repetitions to imprint human cognition with spatial visual­

ization principles.

2. Repeat this study and add a fourth instructional treatment

group. Group 4 would then receive instruction that uses the glass

box and the bowl/hemisphere imagery simultaneously. Each image

would be used to complement the other in a holistic way that is in

keeping with Gestaltic concepts identified by Gibson (1969). And as

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. such the possibility of a new and higher level of learner under­

standing ( i.e ., insight) is created.

3. Conduct a study similar to this one with manual drafting

laboratory exercises added. Help given to the subjects of this

proposed study would be imagery specific (i.e ., glass box or bowl/

hemisphere). The laboratory exercises would be graded, thereby,

adding some importance to the visualization process. The physical

act of drawing with pencil and paper helps an individual to access

the right hemispheric side of their brain (Edwards, 1989). And the

right hemispheric side of the brain is known to often contain non­

temporal, spatial, and holistic cognitive functions; each of which

has been shown to positively affect spatial visualization.

4. Conduct a survey of several hundred experienced drafters,

designers, engineers, technical illustrators, and artists to deter­

mine how they spatially visualize and mentally rotate three-

dimensional objects prior to creating two-dimensional drawings. A

study of this type may discover new spatial visualization imagery

methods or point to the most appropriate existing method for teach­

ing multiview orthographic projection.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDICES

71

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendix A

Definition of Terms

72

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73

Definition of Terms

The following definitions for terms used in this study will

provide a common basis of understanding.

Bowl/hemispheric method: An unconventional method of teaching

orthographic projection in which an object is placed in the middle

of a bowl or hemispheric shape. The front view of the object is

viewed by looking directly into the bowl from above. Other views

are developed by sliding the object along the surface of the bowl

until another side of the object is fu lly exposed (see Figure 1).

Cognition: All our mental abi1itie s —-perceiving, remembering,

reasoning, and many others--are organized into a complex system, the

overall function of which is termed cognition (Glass, Holyoak, &

Santa, 1979).

Field dependence: A lack of ability to impose structure on an

unorganized or camouflaged perceptual field .

Field independence: The ability to impose structure on an

unorganized perceptual field (Dahl, 1984).

First-angle projection: A form of orthographic projection used

in Europe in which the object appears between the plane of projec­

tion and the viewer's line of sight.

F lexib ility of closure: The ab ility to hold a given visual

precept or configuration in mind so as to disembed it from other

well-defined perceptual material (Ekstrom, French, & Harmon, 1976).

Hinged glass box method: A method of teaching multiview

orthographic projection in which an object is placed inside a real

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. or imaginary hinged glass box. After the object has been projected

and drawn on all sides of the glass box, it is unfolded into a

single two-dimensional surface showing each view of the object in

relationship to one another (see Figure 1).

Left brain: The left hemispheric side of the brain, generally

including verbal, analytic, symbolic, abstract, temporal, rational,

digital, logical, and linear cognitive functions, which is dominant

in the majority of individuals.

Multi view orthographic projection: The representation of re­

lated views of an object as if they were all in the same plane and

projected by orthographic projection.

Nonvisual: An arbitrary designation given to individuals who

score poorly on one or more standardized tests for varying forms of

visual cognition.

Orthographic projection: Projection of a single view in which

the view is projected along lines perpendicular to both the view and

the drawing surface.

Right brain: The right hemispheric side of the brain, gener­

ally including nonverbal, synthetic, concrete analogic, nontemporal,

nonrational, spatial, intuitive, and holistic cognitive functions,

which is dominant in some individuals.

Spatial visualization: The aptitude to comprehend imaginary

movement of an object in three-dimensional space.

Speed of closure: The ability to unite an apparently disparate

perceptual field into a single concept (Ekstrom et a l., 1976).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Third angle projection; A form of orthographic projection used

in the United States in which the plane of projection appears

between the object and the viewer's line of sight.

Vi sual: An arbitrary designation given to individuals who

score well on one or more standardized tests for varying forms of

visual cognition.

Visualization: The ability to manipulate or transform the

image of spatial patterns into other arrangements (Ekstrom et a l.,

1976).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendix B

Recruitment Script

76

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77

SUBJECT SELECTION PROCEDURE ORAL PRESENTATION

Recruitment Script

I am conducting a formal research study through Western Michi­ gan University as part of my doctoral dissertation. The purpose of the study will be to compare the effectiveness of using two methods of teaching multiview orthographic projection to college students with varying levels of spatial visualization ability.

Because generalized results of this study will be published, participants must be volunteers. I am seeking volunteers from this class. Each volunteer will be asked to take three short tests with a total time commitment of 70 minutes.

Participation or nonparticipation in the study will have no influence on your course grade. If you volunteer, you may discontinue your participation in this study at any time without jeopardizing your relationship with Western Michigan University, Ferris State University, or without influencing your grade.

Your willingness to participate in this research study must be indicated by your signature on the consent form soon to be passed out. Please read it carefully before signing. If you do not wish to participate in this study, sign a made-up name instead of your real name. Then fold the consent form in half for collection. Thank you.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendix C

Consent Form

78

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79

CONSENT FORM

Mr. Mark A. Curtis of Ferris State University is conducting a formal experimental research study through Western Michigan University as part of his doctoral dissertation. The purpose of the study, which takes place over a two week period, will be to compare the effectiveness of using two methods of teaching multi­ view orthographic projection to college students with varying levels of spatial visualization ability.

Data collected in this study will be used to Judge the relative worth of two different instructional methodologies. Data will be collected via three tests with a total time committment of 70 minutes. Data collection procedures, exposure to the tests and instructional methodologies involve no forseeable hazard or risk to the participants. This study may provide benefits to future engineering graphics educators and students alike by proving that certain students can be taught more effectively using one visualization technique versus another.

Participation in this study is strictly voluntary. Participation or nonparticipation in this study will have no influence on your course grade. If you volunteer, you may discontinue your participation in this study at any time without Jeopardizing your relationship with Western Michigan University or Ferris State University or your course grade. Special measures have been taken to insure the confidentiality of all participants (approximately 90). If questions or problems should arise relating to this study, the fallowing individuals may be contacted:

Dr. Ken Dickie Dr. Ray Cross Professor, Head, Manufacturing Educational Leadership Engineering Technologies Western Michigan University Ferris State University Kalamazoo, MI 49008 Big Rapids, MI 49307 (616) 387-3884 (616) 592-2511

Your willingness to voluntarily participate in this research study must be indicated by your signing and dating this consent form in the space provided below. If you do not wish to participate in this study, sign a made-up name instead of your real name or simply do not sign the consent form at all.

Signature Date

Now, please fold the form in half for collection. Thank You.

Mark A. Curtis

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendix D

Differential Aptitude Test Space Relations Form T Directions and Examples

80

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. THE PSYCHOLOGICAL CORPORATION-' 555 ACAPEMIC COURT, SAN ANTONIO, TEXAS 78204-2498 TELEPHONE: (512) 299-1001 TELEX: 5I060I5629 TPCSAT FAX: (512) 270-0327

November 7, 1991

Mark A. Curtis Graduate Student c/o Mfg. Eng. Technologies Dept. Ferris State University Big Rapids, MI 49307

Dear Mr. Curtis:

Thank you for your November 1 fax containing your order for the Differential Aptitude Test material for testing purposes in your dissertation research.

In order to protect the combined usefulness of the test, and as a responsible test publisher, we believe it is our responsibility to maintain the security and Integrity of our tests. Consequently, we cannot allow items or portions of the test to be bound in, stapled with or microfilmed with your dissertation. Sample items may be bound, but actual test items cannot and must be referred to by page and/or item number as stated in the test.

In addition, all testing should be conducted in your presence or that of your faculty advisor so that all test materials remain in your hands.

We will gladly grant permission for use of the test if the above restrictions will be adhered to. Please indicate agreement to the above terms by signing and returning a copy of this letter to me for my files. I will release your order upon receipt of the signed document.

Also, please forward a copy of your dissertation when it is completed so that I may retain a copy in our library. If you have any questions regarding the above please contact me directly.

Sincerely,

Christine Doebbler Supervisor Rights and Permissions

UNDERSTOOD AND AGREED

Name Date HARCOURT BRACE JOVANOVICH, INC.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 82

I; DO NO fcM AKE :ANYi, f MARK YOUR ANSWERS S^^^HE.'sE^ARATEit SPACE RELATIONS .^ANSW ER 8HBETVri Brito iV»W->.—

DIRECTIONS

Find the place for Space Relations on the Answer Sheet. This test consists of 60 patterns which can be folded into figures. To the right of each pattern there are four figures. You are to decide which one of these figures can be made from the pattern shown. The pattern always shows the outside of the figure. Here is an example:

Example X.

Oi

In Example X, which one of the four figures—A, B, C, D —can be made from the pattern at the left? A and B certainly cannot be made; they are not the right shape. C is correct both in shape and size. You cannot make D from this pattern. Therefore, the space under C has been filled in on line X of your Answer Sheet.

Remember: In this test there will always be a row of four figures following each pattern. In every row there is only one correct figure.

N ow look at Example Y on the next page.

Copyright 1947, © 1961, 1962, 1972 by The Psychological Corporation.

A ll rights reserved. No part or the test In this booklet may be reproduced in any form of printing or by any other means, electronic or mechanical, including, but not limited to, photocopying, audiovisual recording and transmission, and portrayal or duplication in any information storage and retrieval system, without permission in w riting from the publisher. The test contained in this booklet Is designed for use only with answer media published or authorized by The Psychological Corporation. If other answer media are used. The Psychological Corporation can take no responsibility for the meaningfulness o f scores. Printed in U.S.A. The Psychological Corporation, New York, N .Y. 10017 73*163TB-

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Example Y.

In Example Y all the figures next to the pattern are correct in shape, but only one of them can be made from this pattern. Note that when the pattern is folded, the figure it makes will have three gray surfaces. Two of these will be the largest surfaces, either of which could be the top or the bottom of a box. The other will be one of the smallest surfaces, which would be one end of the box.

Now look at the four figures: Figure A is wrong. The long, narrow side is not gray in the pattern and the largest surface must be gray. Figure B is wrong. The largest surface must be gray, although the gray end could be at the back. Figure C is wrong. The gray top and end arc all right, but there is no long gray side in the pattern. Figure D is correct. A large gray surface is shown as the top, and the end surface shown is also gray.

So, you see, all four figures are correct in shape, but only one—D —shows the gray surfaces cor­ rectly. Therefore, the space under D has been filled in on line Y of your Answer Sheet.

Remember: The surface you see in the pattern must always be the outside surface of the com­ pleted figure. Study the pattern carefully and decide which figure can be made from it. Only one of the four figures following the pattern is correct. Show your choice on the Answer Sheet by filling in the space under the letter which is the same as that of the figure you have chosen.

You will have 25 minutes for this test. W ork as rapidly and as accurately as you can. If you are not sure of an answer, mark the choice which is your best guess.

DO NOT TURN THE PAGE UNTIL YOU ARE TOLD TO DO SO.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendix E

Western Michigan University Diagnostic/Achievement Quiz, Spatial Perception, Directions, and Example

84

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Testing and Evaluation Services Kalamazoo. Michigan 49008-3853 616 387-3905

W e s t e r n M ic h ig a n U n iv e r s it y

Mark A. Curtis January 10, 1992 15364 Clear Lake Drive Big Rapids, MI 49307

Dear Mark:

I recently received your request for written permission to use

the Western Michigan University Diagnostic/Achievement Quiz, Part

#3, Spatial Perception in your dissertation research. You have

my permission to use this portion of the quiz in your research

and paper. If you wish, you may include the instructions and

related example problems within the appendix of your

dissertation. Since this instrument is copyrighted, I would hope

that any individuals reading your paper would realize they cannot

duplicate our items without similar permission. Best of luck to

you, and I hope you will send me a copy of your completed

dissertation for our historical records.

Sincerely,

Gerard T. Nowak Associate Director

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DiagnosticlAchievement Quiz

PART 3 SPATIAL PERCEPTION Directions

The problems in Part 3 make use of three-view drawings. A three-view drawing is a drawing of an object that shows three different views (or pictures) of an object. One view is of the object’s front, one is of its top, and one is of its side. On the three-view drawing the top view is drawn above the front view, and the side view is drawn to the right of the front view.

Look at the three dimensional drawings of Objects A and B below. The drawings show the positions a person would have to be in to see the front, top, and side views of the objects. Next to each illustration is the three-view drawing of the object.

Top View Three-view drawing of Object A

Top View

Fronc View Object Side View J£ isy Side View

Three-View Top View drawing of Object B

Fronc View Object B Fronc View Side View

Go to the next page.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Career Guidance Inventory

Each of the problems in Part 3 shows a three-view drawing of an object with one view missing. (The three dimensional illustration of the object is not shown.) You are to select the correct missing view out of the five choices shown to the right of each three-view drawing. Look at the example below and then do the problems in Part 3. Record your answers on the answer sheet beginning with number 229.

EXAMPLE

1.

5 is the correct missing view 1 2 3 4 5 1oooo® If you feel unable to answer the questions in this part, feel free to skip this section after looking carefully at the explanation drawing, the examples and all the problems. Many people will not be able to answer any of the items in this section, especially if they do not have a mechanical background; however, you should answer as many of the items as you can.

When you finish this section you will have completed the Diagnostic/Achievement Quiz.

Begin on page 47, starting with number 229.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendix F

Correlation Data for Two Pretests

88

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 89

Pretest Correlation Data

Pre- DAT-SR-T ortho

17.00 3.00 51.00 289.00 9.00 Group 1 start 21.00 3.00 63.00 441.00 9.00 22.00 1.00 22.00 484.00 1.00 23.00 5.00 115.00 529.00 25.00 32.00 2.00 64.00 1,024.00 4.00 34.00 4.00 136.00 1,156.00 16.00 34.00 4.00 136.00 1,156.00 16.00 35.00 1.00 35.00 1,225.00 1.00 36.00 2.00 72.00 1,296.00 4.00 37.00 5.00 185.00 1,369.00 25.00 38.00 3.00 114.00 1,444.00 9.00 38.00 4.00 152.00 1,444.00 16.00 39.00 3.00 117.00 1,521.00 9.00 40.00 3.00 120.00 1,600.00 9.00 40.00 2.00 80.00 1,600.00 9.00 41.00 3.00 123.00 1,681.00 9.00 42.00 8.00 336.00 1,764.00 64.00 44.00 3.00 132.00 1,936.00 9.00 44.00 5.00 220.00 1,936.00 25.00 44.00 6.00 264.00 1,936.00 36.00 45.00 8.00 360.00 2,025.00 64.00 45.00 8.00 360.00 2,025.00 64.00 46.00 5.00 230.00 2,116.00 25.00 47.00 5.00 235.00 2,209.00 25.00 48.00 7.00 336.00 2,304.00 49.00 50.00 10.00 500.00 2,500.00 100.00 51.00 4.00 204.00 2,601.00 16.00 51.00 4.00 204.00 2,601.00 16.00 51.00 4.00 204.00 2,601.00 16.00 52.00 5.00 260.00 2,704.00 25.00 57.00 9.00 513.00 3,249.00 81.00 Group 1 end _n = 31 18.00 3.00 54.00 324.00 9.00 Group 2 start 21.00 5.00 105.00 441.00 25.00 22.00 0.00 0.00 484.00 0.00 24.00 3.00 72.00 576.00 9.00 34.00 2.00 68.00 1,156.00 4.00 35.00 1.00 35.00 1,225.00 1.00 35.00 3.00 105.00 1,225.00 9.00 36.00 5.00 180.00 1,296.00 25.00 38.00 2.00 76.00 1,444.00 4.00 38.00 4.00 152.00 1,444.00 16.00 38.00 3.00 114.00 1,444.00 9.00 40.00 3.00 120.00 1,600.00 9.00

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 90

Pretest Correlation Data--Continued

Pre- DAT-SR-T ortho

40.00 6.00 240.00 1,600.00 36.00 40.00 3.00 120.00 1,600.00 9.00 41.00 6.00 246.00 1,681.00 36.00 41.00 5.00 205.00 1,681.00 25.00 43.00 1.00 43.00 1,849.00 1.00 44.00 3.00 132.00 1,936.00 9.00 44.00 5.00 220.00 1,936.00 25.00 44.00 4.00 176.00 1,936.00 16.00 45.00 5.00 225.00 2,025.00 25.00 45.00 5.00 225.00 2,025.00 25.00 46.00 6.00 276.00 2,116.00 36.00 48.00 3.00 144.00 2,304.00 9.00 49.00 3.00 147.00 2,401.00 9.00 50.00 6.00 300.00 2,500.00 36.00 51.00 6.00 306.00 2,601.00 36.00 51.00 5.00 255.00 2,601.00 25.00 55.00 4.00 220.00 3,025.00 16.00 55.00 8 .CO 440.00 3,025.00 64.00 57.00 7.00 399.00 3,249.00 49.00 Group 2 end _n = 31 19.00 0.00 0.00 361.00 0.00 Group 3 start 22.00 3.00 66.00 484.00 9.00 24.00 4.00 96.00 576.00 16.00 34.00 2.00 68.00 1,156.00 4.00 35.00 2.00 70.00 1,225.00 4.00 36.00 3.00 108.00 1,296.00 9.00 37.00 7.00 259.00 1,369.00 49.00 37.00 3.00 111.00 1,369.00 9.00 38.00 4.00 152.00 1,444.00 16.00 38.00 2.00 76.00 1,444.00 4.00 38.00 7.00 266.00 1,444.00 49.00 39.00 6.00 234.00 1,521.00 36.00 39.00 3.00 117.00 1,521.00 9.00 39.00 4.00 156.00 1,521.00 16.00 39.00 3.00 117.00 1,521.00 9.00 40.00 2.00 80.00 1,600.00 4.00 40.00 3.00 120.00 1,600.00 9.00 40.00 4.00 160.00 1,600.00 16.00 40.00 2.00 80.00 1,600.00 4.00 42.00 3.00 126.00 1,764.00 9.00 44.00 5.00 220.00 1,936.00 25.00 46.00 5.00 230.00 2,116.00 25.00 46.00 4.00 184.00 2,116.00 16.00 47.00 5.00 235.00 2,209.00 25.00 48.00 3.00 144.00 2,304.00 9.00

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 91

Pretest Correlation Data--Continued

Pre­ DAT-SR-T ortho

48.00 3.00 144.00 2,304.00 9.00 49.00 4.00 196.00 2,401.00 16.00 52.00 8.00 416.00 2,704.00 64.00 55.00 4.00 220.00 3,025.00 16.00 57.00 6.00 342.00 3,249.00 36.00 Group 3 end ji = 30 3,720.00 378.00 16,136.00 158,296.00 1,915.00 Totals X Y XY X(X) Y(Y)

1,244.00 139.00 n = 31 52,766.00 786.00 Group 1 sums 1,268.00 125.00 n = 31 54,750.00 607.00 Group 2 sums 1,208.00 114.00 _n = 30 50,780.00 522.00 Group 3 sums

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendix G

Pretest/Posttest/Gain for Standard Deviation Calculation Data

92

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Pretest/Posttest/Gain for Standard Deviation Calculation Data

Pre Post Gain Pretest Posttest Gain (Pre) (Post) (Gain)

3.00 3.00 0.00 9.00 9.00 0.00 Group 1 start 1.00 1.00 0.00 1.00 1.00 0.00 5.00 4.00 -1.00 25.00 16.00 1.00 2.00 5.00 3.00 4.00 25.00 9.00 4.00 6.00 2.00 16.00 36.00 4.00 4.00 5.00 1.00 16.00 25.00 1.00 1.00 4.00 3.00 1.00 16.00 9.00 2.00 5.00 3.00 4.00 25.00 9.00 5.00 2.00 -3.00 25.00 4.00 9.00 3.00 3.00 0.00 9.00 9.00 0.00 4.00 2.00 -2.00 16.00 4.00 4.00 3.00 6.00 3.00 9.00 36.00 9.00 3.00 3.00 0.00 9.00 9.00 0.00 2.00 7.00 5.00 4.00 49.00 25.00 3.00 5.00 2.00 9.00 25.00 4.00 8.00 10.00 2.00 64.00 100.00 4.00 3.00 5.00 2.00 9.00 25.00 4.00 5.00 5.00 0.00 25.00 25.00 0.00 6.00 4.00 -2.00 36.00 16.00 4.00 8.00 7.00 -1.00 64.00 49.00 1.00 8.00 9.00 1.00 64.00 81.00 1.00 5.00 8.00 3.00 25.00 64.00 9.00 5.00 6.00 1.00 25.00 36.00 1.00 7.00 9.00 2.00 49.00 81.00 4.00 10.00 10.00 0.00 100.00 100.00 0.00 4.00 5.00 1.00 16.00 25.00 1.00 4.00 6.00 2.00 16.00 36.00 4.00 4.00 6.00 2.00 16.00 36.00 4.00 5.00 5.00 0.00 25.00 25.00 0.00 9.00 10.00 1.00 81.00 100.00 1.00 Group 1 end 136.00 166.00 30.00 772.00 1,088.00 122.00 Sums n = 30

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Pretest/Posttest/Gain for Standard Deviation Calculation Data

Pre Post Gain Pretest Posttest Gain (Pre) (Post) (Gain)

3.00 5.00 2.00 9.00 25.00 4.00 Group 2 start 5.00 6.00 1.00 25.00 36.00 1.00 0.00 2.00 2.00 0.00 4.00 4.00 3.00 4.00 1.00 9.00 16.00 1.00 2.00 4.00 2.00 4.00 16.00 4.00 1.00 2.00 1.00 1.00 4.00 1.00 3.00 5.00 2.00 9.00 25.00 4.00 5.00 4.00 -1.00 25.00 16.00 1.00 2.00 4.00 2.00 4.00 16.00 4.00 3.00 4.00 1.00 9.00 16.00 1.00 3.00 3.00 0.00 9.00 9.00 0.00 6.00 6.00 0.00 36.00 36.00 0.00 3.00 7.00 4.00 9.00 49.00 16.00 6.00 2.00 -4.00 36.00 2.00 16.00 5.00 4.00 -1.00 25.00 16.00 1.00 1.00 5.00 4.00 1.00 25.00 16.00 3.00 6.00 3.00 9.00 36.00 9.00 5.00 3.00 -2.00 25.00 9.00 2.00 4.00 4.00 0.00 16.00 16.00 0.00 5.00 6.00 1.00 25.00 36.00 1.00 6.00 7.00 1.00 36.00 49.00 1.00 3.00 4.00 1.00 9.00 16.00 1.00 3.00 2.00 -1.00 9.00 4.00 1.00 6.00 5.00 -1.00 36.00 25.00 1.00 6.00 10.00 4.00 36.00 100.00 16.00 5.00 7.00 2.00 25.00 49.00 4.00 4.00 5.00 1.00 16.00 25.00 1.00 8.00 6.00 -2.00 64.00 36.00 4.00 7.00 9.00 2.00 49.00 81.00 4.00 Group 2 end 116.00 141.00 25.00 566.00 793.00 119.00 Sums n = 29

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 95

Pretest/Posttest/Gain for Standard Deviation Calculation Data

Pre Post Gain Pretest Posttest Gain (Pre) (Post) (Gain)

0.00 4.00 4.00 0.00 16.00 16.00 Group 3 start 3.00 2.00 -1.00 9.00 4.00 1.00 4.00 2.00 -2.00 16.00 4.00 4.00 2.00 4.00 2.00 4.00 16.00 4.00 3.00 6.00 3.00 9.00 36.00 9.00 7.00 5.00 -2.00 49.00 25.00 4.00 3.00 6.00 3.00 9.00 36.00 9.00 4.00 2.00 -2.00 16.00 4.00 4.00 2.00 3.00 1.00 4.00 9.00 1.00 7.00 5.00 -2.00 49.00 25.00 4.00 6.00 4.00 -2.00 36.00 16.00 4.00 3.00 4.00 1.00 9.00 16.00 1.00 4.00 5.00 1.00 16.00 25.00 1.00 3.00 3.00 0.00 9.00 9.00 0.00 2.00 6.00 4.00 4.00 36.00 16.00 3.00 4.00 1.00 9.00 16.00 1.00 4.00 2.00 -2.00 16.00 4.00 4.00 3.00 5.00 2.00 9.00 25.00 4.00 5.00 2.00 -3.00 25.00 4.00 9.00 4.00 4.00 0.00 16.00 16.00 0.00 5.00 7.00 2.00 25.00 49.00 4.00 3.00 3.00 0.00 9.00 9.00 0.00 3.00 6.00 3.00 9.00 36.00 9.00 4.00 2.00 -2.00 16.00 4.00 4.00 8.00 10.00 2.00 64.00 100.00 4.00 4.00 5.00 1.00 16.00 25.00 1.00 6.00 6.00 0.00 36.00 36.00 0.00 Group 3 end 105.00 117.00 12.00 489.00 601.00 118.00 Sums n = 27

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendix H

Complete Raw Data by Subject, Test, Group, and Aptitude Level

96

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 97

Complete Raw Data by Subject, Test, Group, and Aptitude Level

Pre­ Post­ ubject DAT-SR-T ortho ortho Group Aptitude

1 17.00 __ 2 21.00 3.00 3.00 1 1 Low 3 22.00 1.00 1.00 1 1 4 23.00 5.00 4.00 1 1 5 32.00 2.00 5.00 1 1 6 34.00 4.00 6.00 1 1 7 34.00 4.00 5.00 1 1 8 35.00 1.00 4.00 1 1 9 36.00 2.00 5.00 1 2 Middle 10 37.00 5.00 2.00 1 2 11 38.00 3.00 3.00 1 2 12 38.00 4.00 2.00 1 2 13 39.00 3.00 6.00 1 2 14 40.00 3.00 3.00 1 2 15 40.00 2.00 7.00 1 2 16 41.00 3.00 5.00 1 3 Middle 17 42.00 8.00 10.00 1 3 18 44.00 3.00 5.00 1 3 19 44.00 5.00 5.00 1 3 20 44.00 6.00 4.00 1 3 21 45.00 8.00 7.00 1 3 22 45.00 8.00 9.00 1 3 23 46.00 5.00 8.00 1 3 24 47.00 5.00 6.00 1 4 High 25 48.00 7.00 9.00 1 4 26 50.00 10.00 10.00 1 4 27 51.00 4.00 5.00 1 4 28 51.00 4.00 6.00 1 4 29 51.00 4.00 6.00 1 4 30 52.00 5.00 5.00 1 4 31 57.00 9.00 10.00 1 4 1,244.00 136.00 166.00

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 98

Complete Raw Data by Subject, Test, Group, and Aptitude Level

Pre­ Post­ ubject DAT-SR-T ortho ortho Group Apt i

1 18.00 3.00 5.00 2 1 Low 2 21.00 5.00 6.00 2 1 3 22.00 0.00 2.00 2 1 4 24.00 3.00 4.00 2 1 5 34.00 2.00 4.00 2 1 6 35.00 1.00 2.00 2 1 7 35.00 3.00 5.00 2 1 8 36.00 5.00 4.00 2 2 Middle low 9 38.00 2.00 4.00 2 2 10 38.00 — 2 - 11 38.00 3.00 4.00 2 2 12 40.00 3.00 3.00 2 2 13 40.00 6.00 6.00 2 2 14 40.00 3.00 7.00 2 2 15 41.00 6.00 2.00 2 3 Middle high 16 41.00 5.00 4.00 2 3 17 43.CO 1.00 5.00 2 3 18 44.00 3.00 6.00 2 3 19 44.00 5.00 3.00 2 3 20 44.00 4.00 4.00 2 3 21 45.00 —— 2 - 22 45.00 5.00 6.00 2 3 23 46.00 6.00 7.00 2 3 24 48.00 3.00 4.00 2 4 High 25 49.00 3.00 2.00 2 4 26 50.00 6.00 5.00 2 4 27 51.00 6.00 10.00 2 4 28 51.00 5.00 7.00 2 4 29 55.00 4.00 5.00 2 4 30 55.00 8.00 6.00 2 4 31 57.00 7.00 9.00 2 4 1,268.00 116.00 141.00

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 99

Complete Raw Data by Subject, Test, Group, and Aptitude Level

Pre­ Post­ ubject DAT-SR-T ortho ortho Group Apt i

1 19.00 0.00 4.00 3 1 Low 2 22.00 3.00 2.00 3 1 3 24.00 4.00 2.00 3 1 4 34.00 -- — 3 - 5 35.00 2.00 4.00 3 1 6 36.00 3.00 6.00 3 2 Middle low 7 37.00 7.00 5.00 3 2 8 37.00 3.00 6.00 3 2 9 38.00 4.00 2.00 3 2 10 38.00 2.00 3.00 3 2 11 38.00 7.00 5.00 3 2 12 39.00 6.00 4.00 3 2 13 39.00 3.00 4.00 3 2 14 39.00 4.00 5.00 3 2 15 39.00 3.00 3.00 3 2 16 40.00 2.00 6.00 3 2 17 40.00 3.00 4.00 3 2 18 40.00 4.00 2.00 3 2 19 40.00 -- — 3 - 20 42.00 3.00 5.00 3 3 Middle high 21 44.00 5.00 2.00 3 3 22 46.00 -- — 3 - 23 46.00 4.00 4.00 3 3 24 47.00 5.00 7.00 3 4 High 25 48.00 3.00 3.00 3 4 26 48.00 3.00 6.00 3 4 27 49.00 4.00 2.00 3 4 28 52.00 8.00 10.00 3 4 29 55.00 4.00 5.00 3 4 30 57.00 6.00 6.00 3 4 1,208.00 105.00 117.00

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendix I

Approval Letter From Western Michigan University Human Subjects Institutional Review Board

100

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Human Subjects Institutional Review Board

WESTERN MICHIGAN UNIVERSITY

Dale: December 11, 1991

To: Mark Curtis

From: Mary Anne Bunda, Chair ' / t f a

Re: HSIRB Project Number 91-11-06

This letter will serve as confirmation that your research protocol, "Spatial visualization and teaching multlvlew orthographic projectlpon: An alternative to the glass box" has been approved after expedited review by a subcommittee of the HSIRB. The conditions and duration of this approval are specified In the Policies of Western Michigan University. You may now begin to implement the research as described in the approval application.

You must seek reapproval for any change In this design. You must also seek reapproval if the project extends beyond the termination date.

The Board wishes you success In the pursuit of your research goals.

xc: Dickie, EDLD

Approval Termination: December 11, 1992

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